Mixing patterns in networks

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.

Network ecology: Tie fitness in social context(s)

Social relations are embedded in material, cultural, and institutional settings that affect network dynamics and the resulting topologies. For example, romantic entanglements are subject to social and cultural norms, interfirm alliances are constrained by country-specific legislation, and adolescent friendships are conditioned by classroom settings and neighborhood effects. In short, social contexts shape social relations and the networks they give rise to. However, how and when they do so remain to be established. This paper presents network ecology as a general framework for identifying how the proximal environment shapes social networks by focusing interactions and social relations, and how these interactions and relations in turn shape the environment in which social networks form. Tie fitness is introduced as a metric that quantifies how well particular dyadic social relations would align with the setting. Using longitudinal networks collected on two cohorts each in 18 North American schools, i.e., 36 settings, we develop five generalizable observations about the time-varying fitness of adolescent friendship. Across all 252 analyzed networks, tie fitness predicted new tie formation, tie longevity, and tie survival. Dormant fit ties cluster in relational niches, thereby establishing a resource base for social identities competing for increased representation in the relational system.

Using Complex Networks in the Hearing Sciences

In this Point of View, we review a number of recent discoveries from the emerging, interdisciplinary field of Network Science , which uses graph theoretic techniques to understand complex systems. In the network science approach, nodes represent entities in a system, and connections are placed between nodes that are related to each other to form a web-like network . We discuss several studies that demonstrate how the micro-, meso-, and macro-level structure of a network of phonological word-forms influence spoken word recognition in listeners with normal hearing and in listeners with hearing loss. Given the discoveries made possible by this new approach and the influence of several complex network measures on spoken word recognition performance we argue that speech recognition measures-originally developed in the late 1940s and routinely used in clinical audiometry-should be revised to reflect our current understanding of spoken word recognition. We also discuss other ways in which the tools of network science can be used in Speech and Hearing Sciences and Audiology more broadly.

Spatiotemporal-social association predicts immunological similarity in rewilded mice

Environmental influences on immune phenotypes are well-documented, but our understanding of which elements of the environment affect immune systems, and how, remains vague. Behaviors, including socializing with others, are central to an individual's interaction with its environment. We therefore tracked behavior of rewilded laboratory mice of three inbred strains in outdoor enclosures and examined contributions of behavior, including associations measured from spatiotemporal co-occurrences, to immune phenotypes. We found extensive variation in individual and social behavior among and within mouse strains upon rewilding. In addition, we found that the more associated two individuals were, the more similar their immune phenotypes were. Spatiotemporal association was particularly predictive of similar memory T and B cell profiles and was more influential than sibling relationships or shared infection status. These results highlight the importance of shared spatiotemporal activity patterns and/or social networks for immune phenotype and suggest potential immunological correlates of social life.

Graph theory analysis reveals an assortative pain network vulnerable to attacks

The neural substrate of pain experience has been described as a dense network of connected brain regions. However, the connectivity pattern of these brain regions remains elusive, precluding a deeper understanding of how pain emerges from the structural connectivity. Here, we employ graph theory to systematically characterize the architecture of a comprehensive pain network, including both cortical and subcortical brain areas. This structural brain network consists of 49 nodes denoting pain-related brain areas, linked by edges representing their relative incoming and outgoing axonal projection strengths. Within this network, 63% of brain areas share reciprocal connections, reflecting a dense network. The clustering coefficient, a measurement of the probability that adjacent nodes are connected, indicates that brain areas in the pain network tend to cluster together. Community detection, the process of discovering cohesive groups in complex networks, successfully reveals two known subnetworks that specifically mediate the sensory and affective components of pain, respectively. Assortativity analysis, which evaluates the tendency of nodes to connect with other nodes that have similar features, indicates that the pain network is assortative. Finally, robustness, the resistance of a complex network to failures and perturbations, indicates that the pain network displays a high degree of error tolerance (local failure rarely affects the global information carried by the network) but is vulnerable to attacks (selective removal of hub nodes critically changes network connectivity). Taken together, graph theory analysis unveils an assortative structural pain network in the brain that processes nociceptive information. Furthermore, the vulnerability of this network to attack presents the possibility of alleviating pain by targeting the most connected brain areas in the network.

Beyond scale-free networks: integrating multilayer social networks with molecular clusters in the local spread of COVID-19

This study evaluates the scale-free network assumption commonly used in COVID-19 epidemiology, using empirical social network data from SARS-CoV-2 Delta variant molecular local clusters in Houston, Texas. We constructed genome-informed social networks from contact and co-residence data, tested them for scale-free power-law distributions that imply highly connected hubs, and compared them to alternative models (exponential, log-normal, power-law with exponential cutoff, and Weibull) that suggest more evenly distributed network connections. Although the power-law model failed the goodness of fit test, after incorporating social network ties, the power-law model was at least as good as, if not better than, the alternatives, implying the presence of both hub and non-hub mechanisms in local SARS-CoV-2 transmission. These findings enhance our understanding of the complex social interactions that drive SARS-CoV-2 transmission, thereby informing more effective public health interventions.

Towards a biologically annotated brain connectome

The brain is a network of interleaved neural circuits. In modern connectomics, brain connectivity is typically encoded as a network of nodes and edges, abstracting away the rich biological detail of local neuronal populations. Yet biological annotations for network nodes - such as gene expression, cytoarchitecture, neurotransmitter receptors or intrinsic dynamics - can be readily measured and overlaid on network models. Here we review how connectomes can be represented and analysed as annotated networks. Annotated connectomes allow us to reconceptualize architectural features of networks and to relate the connection patterns of brain regions to their underlying biology. Emerging work demonstrates that annotated connectomes help to make more veridical models of brain network formation, neural dynamics and disease propagation. Finally, annotations can be used to infer entirely new inter-regional relationships and to construct new types of network that complement existing connectome representations. In summary, biologically annotated connectomes offer a compelling way to study neural wiring in concert with local biological features.

A Mixed-Method Social Network Analysis of Low-Income Diverse Older Volunteers

Although volunteering has been associated with numerous social benefits for diverse older adults, there is little information on how they establish relationships within a multicultural volunteering program outside of their co-ethnic communities. This convergent mixed-method social network study adopts the bonding and bridging social capital theory to explore the structures and dynamics of social interactions within a multicultural volunteer program. Low-income Russian, Khmer, Somali, Nepali, and English-speaking older volunteers in the Senior Companions Program (SCP) in a Midwest metropolitan (N = 83) participated in the surveys and focus groups. Homophily coefficients (r) show that the SCP volunteers mostly interacted with people who identified with the same nationality (r = .86), race (r = .87), and gender (r = .50). Qualitative results suggested that volunteers strengthened their social networks through within-cultural social bonding while appreciating opportunities for cross-cultural social bridging. Compared with within-cultural social bonding, cross-cultural social bridging in multicultural volunteer programs require intentional facilitation, resources, and organizational commitment.

On the inadequacy of nominal assortativity for assessing homophily in networks

Nominal assortativity (or discrete assortativity) is widely used to characterize group mixing patterns and homophily in networks, enabling researchers to analyze how groups interact with one another. Here we demonstrate that the measure presents severe shortcomings when applied to networks with unequal group sizes and asymmetric mixing. We characterize these shortcomings analytically and use synthetic and empirical networks to show that nominal assortativity fails to account for group imbalance and asymmetric group interactions, thereby producing an inaccurate characterization of mixing patterns. We propose the adjusted nominal assortativity and show that this adjustment recovers the expected assortativity in networks with various level of mixing. Furthermore, we propose an analytical method to assess asymmetric mixing by estimating the tendency of inter- and intra-group connectivities. Finally, we discuss how this approach enables uncovering hidden mixing patterns in real-world networks.

The enmity paradox

The "friendship paradox" of social networks states that, on average, "your friends have more friends than you do". Here, we theoretically and empirically explore a related and overlooked paradox we refer to as the "enmity paradox". We use empirical data from 24,678 people living in 176 villages in rural Honduras. We empirically show that, for a real negative undirected network (created by symmetrizing antagonistic interactions), the paradox exists as it does in the positive world. Specifically, a person's enemies have more enemies, on average, than a person does. Furthermore, in a mixed world of positive and negative ties, we study the conditions for the existence of the paradox, which we refer to as the "mixed-world paradox", both theoretically and empirically, finding that, for instance, a person's friends typically have more enemies than a person does. We also confirm the "generalized" enmity paradox for non-topological attributes in real data, analogous to the generalized friendship paradox (e.g., the claim that a person's enemies are richer, on average, than a person is). As a consequence, the naturally occurring variance in the degree distribution of both friendship and antagonism in social networks can skew people's perceptions of the social world.

Modular tipping points: How local network structure impacts critical transitions in networked spin systems

Critical transitions describe a phenomenon where a system abruptly shifts from one stable state to an alternative, often detrimental, stable state. Understanding and possibly preventing the occurrence of a critical transition is thus highly relevant to many ecological, sociological, and physical systems. In this context, it has been shown that the underlying network structure of a system heavily impacts the transition behavior of that system. In this paper, we study a crucial but often overlooked aspect in critical transitions: the modularity of the system's underlying network topology. In particular, we investigate how the transition behavior of a networked system changes as we alter the local network structure of the system through controlled changes of the degree assortativity. We observe that systems with high modularity undergo cascading transitions, while systems with low modularity undergo more unified transitions. We also observe that networked systems that consist of nodes with varying degrees of connectivity tend to transition earlier in response to changes in a control parameter than one would anticipate based solely on the average degree of that network. However, in rare cases, such as when there is both low modularity and high degree disassortativity, the transition behavior aligns with what we would expected given the network's average degree. Results are confirmed for a diverse set of degree distributions including stylized two-degree networks, uniform, Poisson, and power-law degree distributions. On the basis of these results, we argue that to understand critical transitions in networked systems, they must be understood in terms of individual system components and their roles within the network structure.

Network homophily via tail inequalities

Homophily is the principle whereby "similarity breeds connections." We give a quantitative formulation of this principle within networks. Given a network and a labeled partition of its vertices, the vector indexed by each class of the partition, whose entries are the number of edges of the subgraphs induced by the corresponding classes, is viewed as the observed outcome of the random vector described by picking labeled partitions at random among labeled partitions whose classes have the same cardinalities as the given one. This is the recently introduced random coloring model for network homophily. In this perspective, the value of any homophily score Θ, namely, a nondecreasing real-valued function in the sizes of subgraphs induced by the classes of the partition, evaluated at the observed outcome, can be thought of as the observed value of a random variable. Consequently, according to the score Θ, the input network is homophillic at the significance level α whenever the one-sided tail probability of observing a value of Θ at least as extreme as the observed one is smaller than α. Since, as we show, even approximating α is an NP-hard problem, we resort to classical tails inequality to bound α from above. These upper bounds, obtained by specializing Θ, yield a class of quantifiers of network homophily. Computing the upper bounds requires the knowledge of the covariance matrix of the random vector, which was not previously known within the random coloring model. In this paper we close this gap. Interestingly, the matrix depends on the input partition only through the cardinalities of its classes and depends on the network only through its degrees. Furthermore all the covariances have the same sign, and this sign is a graph invariant. Plugging this structure into the bounds yields a meaningful, easy to compute class of indices for measuring network homophily. As demonstrated in real-world network applications, these indices are effective and reliable, and may lead to discoveries that cannot be captured by the current state of the art.

The modular biochemical reaction network structure of cellular translation

Translation is an essential attribute of all living cells. At the heart of cellular operation, it is a chemical information decoding process that begins with an input string of nucleotides and ends with the synthesis of a specific output string of peptides. The translation process is interconnected with gene expression, physiological regulation, transcription, and responses to signaling molecules, among other cellular functions. Foundational efforts have uncovered a wealth of knowledge about the mechanistic functions of the components of translation and their many interactions between them, but the broader biochemical connections between translation, metabolism and polymer biosynthesis that enable translation to occur have not been comprehensively mapped. Here we present a multilayer graph of biochemical reactions describing the translation, polymer biosynthesis and metabolism networks of an Escherichia coli cell. Intriguingly, the compounds that compose these three layers are distinctly aggregated into three modes regardless of their layer categorization. Multimodal mass distributions are well-known in ecosystems, but this is the first such distribution reported at the biochemical level. The degree distributions of the translation and metabolic networks are each likely to be heavy-tailed, but the polymer biosynthesis network is not. A multimodal mass-degree distribution indicates that the translation and metabolism networks are each distinct, adaptive biochemical modules, and that the gaps between the modes reflect evolved responses to the functional use of metabolite, polypeptide and polynucleotide compounds. The chemical reaction network of cellular translation opens new avenues for exploring complex adaptive phenomena such as percolation and phase changes in biochemical contexts.

Complex network analysis techniques for the early detection of the outbreak of pandemics transmitted through air traffic

Air transport has been identified as one of the primary means whereby COVID-19 spread throughout Europe during the early stages of the pandemic. In this paper we analyse two categories of methods - dynamic network markers (DNMs) and network analysis-based methods - as potential early warning signals for detecting and anticipating COVID-19 outbreaks in Europe on the basis of accuracy regarding the daily confirmed cases. The analysis was carried out from 15 February 2020, around two weeks before the first COVID-19 cases appeared in Europe, and 1 May 2020, approximately two weeks after all the air traffic in Europe had been shut down. Daily European COVID-19 information sourced from the World Health Organization was used, whereas air traffic data from Flightradar24 has been incorporated into the analyses by means of four alternative adjacency matrices. Some DNMs have been discarded since they output multiple time series, which makes it very difficult to interpret their results. The only DNM outputting a single time series does not emulate the COVID-19 trend: it does not detect all the main peaks, which means that peak heights do not match up with the increase in the number of infected people. However, many combinations of network analysis based methods and adjacency matrices output good results (with high accuracy and 20-day advance forecasts), with only minor differences from one to another. The number of edges and the network density methods are slightly better when dynamic flight frequency information is used.

Framework for converting mechanistic network models to probabilistic models

There are two prominent paradigms for the modelling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the second, referred to as the probabilistic approach, one describes a model that specifies the likelihood of observing a given network. Mechanistic models (models developed based on the mechanistic approach) are appealing because they capture scientific processes that are believed to be responsible for network generation; however, they do not easily lend themselves to the use of inferential techniques when compared with probabilistic models. We introduce a general framework for converting a mechanistic network model (MNM) to a probabilistic network model (PNM). The proposed framework makes it possible to identify the essential network properties and their joint probability distribution for some MNMs; doing so makes it possible to address questions such as whether two different mechanistic models generate networks with identical distributions of properties, or whether a network property, such as clustering, is over- or under-represented in the networks generated by the model of interest compared with a reference model. The proposed framework is intended to bridge some of the gap that currently exists between the formulation and representation of mechanistic and PNMs. We also highlight limitations of PNMs that need to be addressed in order to close this gap.

A Global Feature-Rich Network Dataset of Cities and Dashboard for Comprehensive Urban Analyses

Urban network analytics has become an essential tool for understanding and modeling the intricate complexity of cities. We introduce the Urbanity data repository to nurture this growing research field, offering a comprehensive, open spatial network resource spanning 50 major cities in 29 countries worldwide. Our workflow enhances OpenStreetMap networks with 40 + high-resolution indicators from open global sources such as street view imagery, building morphology, urban population, and points of interest, catering to a diverse range of applications across multiple fields. We extract streetscape semantic features from more than four million street view images using computer vision. The dataset's strength lies in its thorough processing and validation at every stage, ensuring data quality and consistency through automated and manual checks. Accompanying the dataset is an interactive, web-based dashboard we developed which facilitates data access to even non-technical stakeholders. Urbanity aids various GeoAI and city comparative analyses, underscoring the growing importance of urban network analytics research.

Estimating contact network properties by integrating multiple data sources associated with infectious diseases

To effectively mitigate the spread of communicable diseases, it is necessary to understand the interactions that enable disease transmission among individuals in a population; we refer to the set of these interactions as a contact network. The structure of the contact network can have profound effects on both the spread of infectious diseases and the effectiveness of control programs. Therefore, understanding the contact network permits more efficient use of resources. Measuring the structure of the network, however, is a challenging problem. We present a Bayesian approach to integrate multiple data sources associated with the transmission of infectious diseases to more precisely and accurately estimate important properties of the contact network. An important aspect of the approach is the use of the congruence class models for networks. We conduct simulation studies modeling pathogens resembling SARS-CoV-2 and HIV to assess the method; subsequently, we apply our approach to HIV data from the University of California San Diego Primary Infection Resource Consortium. Based on simulation studies, we demonstrate that the integration of epidemiological and viral genetic data with risk behavior survey data can lead to large decreases in mean squared error (MSE) in contact network estimates compared to estimates based strictly on risk behavior information. This decrease in MSE is present even in settings where the risk behavior surveys contain measurement error. Through these simulations, we also highlight certain settings where the approach does not improve MSE.

Evolvement patterns of usage in a medium-sized bike-sharing system during the COVID-19 pandemic

The global outbreak of COVID-19 has fundamentally reshaped human mobility. Compared to other modes of transportation, how spatiotemporal patterns of urban bike-sharing have evolved since the outbreak is yet to be fully understood, especially for bike-sharing systems operating on a smaller scale. Taking Pittsburgh as a case study, we examined the changes in spatiotemporal dynamics of shared bike usage from 2019 to 2021. By distinguishing between weekday and weekend usage, we found different temporal patterns between trip volume and duration, and distinct spatial patterns of within- and between-region rides with respect to naturally separated regions. Overall, the results illustrate the resilience and the vital role of bike-sharing during the pandemic, consistent with previous observations on bike-sharing systems of a larger scale. Our study contributes to a comprehensive understanding of bike-sharing that calls for more research on smaller-scale systems under disruptive events such as the pandemic, which can greatly inform decision-makers from smaller sized cities and enable future studies to compare across different urban regions or modes of transportation.

The 2013 Chikungunya outbreak in the Caribbean was structured by the network of cultural relationships among islands

In 2013, the Caribbean underwent an unprecedented epidemic of Chikungunya that affected 29 islands and mainland territories throughout the Caribbean in the first six months. Analysing the spread of the epidemic among the Caribbean islands, we show that the initial patterns of the epidemic can be explained by a network model based on the flight connections among islands. The network does not follow a random graph model and its topology is likely the product of geo-political relationships that generate increased connectedness among locations sharing the same language. Therefore, the infection propagated preferentially among islands that belong to the same cultural domain, irrespective of their human and vector population densities. Importantly, the flight network topology was also a more important determinant of the disease dynamics than the actual volume of traffic. Finally, the severity of the epidemic was found to depend, in the first instance, on which island was initially infected. This investigation shows how a simple epidemic model coupled with an appropriate human mobility model can reproduce the observed epidemiological dynamics. Also, it sheds light on the design of interventions in the face of the emergence of infections in similar settings of naive subpopulations loosely interconnected by host movement. This study delves into the feasibility of developing models to anticipate the emergence of vector-borne infections, showing the importance of network topology, bringing valuable methods for public health officials when planning control policies. Significance statement: The study shows how a simple epidemic model associated with an appropriate human mobility model can reproduce the observed epidemiological dynamics of the 2014 Chikungunya epidemic in the Caribbean region. This model sheds light on the design of interventions in the face of the emergence of infections in similar settings of naive subpopulations loosely interconnected by the host.

Link-Information Augmented Twin Autoencoders for Network Denoising

Removing noisy links from an observed network is a task commonly required for preprocessing real-world network data. However, containing both noisy and clean links, the observed network cannot be treated as a trustworthy information source for supervised learning. Therefore, it is necessary but also technically challenging to detect noisy links in the context of data contamination. To address this issue, in the present article, a two-phased computational model is proposed, called link-information augmented twin autoencoders, which is able to deal with: 1) link information augmentation; 2) link-level contrastive denoising; 3) link information correction. Extensive experiments on six real-world networks verify that the proposed model outperforms other comparable methods in removing noisy links from the observed network so as to recover the real network from the corrupted one very accurately. Extended analyses also provide interpretable evidence to support the superiority of the proposed model for the task of network denoising.

Inclusion unlocks the creative potential of gender diversity in teams

Several studies have highlighted the potential contribution of gender diversity to creativity, also noted challenges stemming from conflicts and a deficit of trust. Thus, we argue that gender diversity requires inclusion as well to see increased collective creativity. We analyzed teams in 4011 video game projects, recording weighted network data from past collaborations. We developed four measures of inclusion, based on de-segregation, strong ties across genders, and the incorporation of women into the core of the team's network. We measured creativity by the distinctiveness of game features compared to prior games. Our results show that gender diversity without inclusion does not contribute to creativity, while at maximal inclusion one standard deviation change in diversity results in .04-.09 standard deviation increase in creativity. On the flipside, at maximal inclusion but low diversity (when there is a 'token' female team member highly integrated in a male network) we see a negative impact on creativity. Considering the history of game projects in a developer firm, we see that adding diversity first, and developing inclusion later can lead to higher diversity and inclusion, compared to the alternative of recruiting developers with already existing cross-gender ties. This suggests that developer firms should encourage building inclusive collaboration ties in-house.

Using molecular network analysis to understand current HIV-1 transmission characteristics in an inland area of Yunnan, China

HIV-1 molecular surveillance provides a new approach to explore transmission risks and targeted interventions. From January to June 2021, 663 newly reported HIV-1 cases were recruited in Zhaotong City, Yunnan Province, China. The distribution characteristics of HIV-1 subtypes and HIV-1 molecular network were analysed. Of 542 successfully subtyped samples, 12 HIV-1 strains were identified. The main strains were CRF08_BC (47.0%, 255/542), CRF01_AE (17.0%, 92/542), CRF07_BC (17.0%, 92/542), URFs (8.7%, 47/542), and CRF85_BC (6.5%, 35/542). CRF08_BC was commonly detected among Zhaotong natives, illiterates, and non-farmers and was mostly detected in Zhaoyang County. CRF01_AE was frequently detected among married and homosexual individuals and mostly detected in Weixin and Zhenxiong counties. Among the 516 pol sequences, 187 (36.2%) were clustered. Zhaotong natives, individuals aged ≥60 years, and illiterate individuals were more likely to be found in the network. Assortativity analysis showed that individuals were more likely to be genetically associated when stratified by age, education level, occupation, and reporting area. The genetic diversity of HIV-1 reflects the complexity of local HIV epidemics. Molecular network analyses revealed the subpopulations to focus on and the characteristics of the risk networks. The results will help optimise local prevention and control strategies.

A Learning Convolutional Neural Network Approach for Network Robustness Prediction

Network robustness is critical for various societal and industrial networks against malicious attacks. In particular, connectivity robustness and controllability robustness reflect how well a networked system can maintain its connectedness and controllability against destructive attacks, which can be quantified by a sequence of values that record the remaining connectivity and controllability of the network after a sequence of node- or edge-removal attacks. Traditionally, robustness is determined by attack simulations, which are computationally very time-consuming or even practically infeasible for large-scale networks. In this article, an improved method for network robustness prediction is developed based on learning feature representation using the convolutional neural network (LFR-CNN). In this scheme, the higher-dimensional network data are compressed into lower-dimensional representations, which are then passed to a convolutional neural network to perform robustness prediction. Extensive experimental studies on both synthetic and real-world networks, both directed and undirected, demonstrate that: 1) the proposed LFR-CNN performs better than other two state-of-the-art prediction methods, with significantly smaller prediction errors; 2) LFR-CNN is insensitive to the variation of the input network size, which significantly extends its applicability; 3) although LFR-CNN needs more time to perform feature learning, it can achieve accurate prediction faster than attack simulations; and 4) LFR-CNN not only accurately predicts the network robustness, but also provides a good indicator for connectivity robustness, better than the classical spectral measures.

Gone with the epidemic? The spatial effects of the Covid-19 on global investment network

The outbreak of Covid-19 epidemic has a prolonged impact on global economic activities. In recent years, many scholars have been motivated to estimate the effects of Covid-19 shock on global foreign direct investment (FDI). However, existing studies have not paid enough attention to the spillover effects caused by the epidemic. Although few academic works have explored the geographic-neighboring spillover effects of epidemic shock on global investment, we further extent the understanding of the spillover effects in an economic network. On the basis of country-month greenfield FDI panels, we construct a spatial Durbin model, and figure out that Covid-19 shock may have positive FDI spillover effects in an economic network via global FDI transfers. Furthermore, we find that such spillovers are greatly conditioned by country-level network position and institutional ties among nations. Our research suggests that global FDI transfers may partly offset economic-adverse effects of the Covid-19 shock. While global countries, especially those in the Global South, should be more closely embedded in the global investment network in such an uncertain environment.

Network analysis of pig movement data as an epidemiological tool: an Austrian case study

Animal movements represent a major risk for the spread of infectious diseases in the domestic swine population. In this study, we adopted methods from social network analysis to explore pig trades in Austria. We used a dataset of daily records of swine movements covering the period 2015-2021. We analyzed the topology of the network and its structural changes over time, including seasonal and long-term variations in the pig production activities. Finally, we studied the temporal dynamics of the network community structure. Our findings show that the Austrian pig production was dominated by small-sized farms while spatial farm density was heterogeneous. The network exhibited a scale-free topology but was very sparse, suggesting a moderate impact of infectious disease outbreaks. However, two regions (Upper Austria and Styria) may present a higher structural vulnerability. The network also showed very high assortativity between holdings from the same federal state. Dynamic community detection revealed a stable behavior of the clusters. Yet trade communities did not correspond to sub-national administrative divisions and may be an alternative zoning approach to managing infectious diseases. Knowledge about the topology, contact patterns, and temporal dynamics of the pig trade network can support optimized risk-based disease control and surveillance strategies.

Democratic governance and global science: A longitudinal analysis of the international research collaboration network

The democracy-science relationship has traditionally been examined through philosophical conjecture and country case studies. There remains limited global-scale empirical research on the topic. This study explores country-level factors related to the dynamics of the global research collaboration network, focusing on structural associations between democratic governance and the strength of international research collaboration ties. This study combines longitudinal data on 170 countries between 2008 and 2017 from the Varieties of Democracy Institute, World Bank Indicators, Scopus, and Web of Science bibliometric data. Methods include descriptive network analysis, temporal exponential random graph models (TERGM), and valued exponential random graph models (VERGM). The results suggest significant positive effects of democratic governance on the formation and strength of international research collaboration ties and homophily between countries with similar levels of democratic governance. The results also show the importance of exogenous factors, such as GDP, population size, and geographical distance, as well as endogenous network factors, including preferential attachment and transitivity.

Assortative mixing in micro-architecturally annotated brain connectomes

The wiring of the brain connects micro-architecturally diverse neuronal populations, but the conventional graph model, which encodes macroscale brain connectivity as a network of nodes and edges, abstracts away the rich biological detail of each regional node. Here, we annotate connectomes with multiple biological attributes and formally study assortative mixing in annotated connectomes. Namely, we quantify the tendency for regions to be connected based on the similarity of their micro-architectural attributes. We perform all experiments using four cortico-cortical connectome datasets from three different species, and consider a range of molecular, cellular, and laminar annotations. We show that mixing between micro-architecturally diverse neuronal populations is supported by long-distance connections and find that the arrangement of connections with respect to biological annotations is associated to patterns of regional functional specialization. By bridging scales of cortical organization, from microscale attributes to macroscale connectivity, this work lays the foundation for next-generation annotated connectomics.

Information transmission velocity-based dynamic hierarchical brain networks

The brain functions as an accurate circuit that regulates information to be sequentially propagated and processed in a hierarchical manner. However, it is still unknown how the brain is hierarchically organized and how information is dynamically propagated during high-level cognition. In this study, we developed a new scheme for quantifying the information transmission velocity (ITV) by combining electroencephalogram (EEG) and diffusion tensor imaging (DTI), and then mapped the cortical ITV network (ITVN) to explore the information transmission mechanism of the human brain. The application in MRI-EEG data of P300 revealed bottom-up and top-down ITVN interactions subserving P300 generation, which was comprised of four hierarchical modules. Among these four modules, information exchange between visual- and attention-activated regions occurred at a high velocity, related cognitive processes could thus be efficiently accomplished due to the heavy myelination of these regions. Moreover, inter-individual variability in P300 was probed to be attributed to the difference in information transmission efficiency of the brain, which may provide new insight into the cognitive degenerations in clinical neurodegenerative disorders, such as Alzheimer's disease, from the transmission velocity perspective. Together, these findings confirm the capacity of ITV to effectively determine the efficiency of information propagation in the brain.

Circulation of a digital community currency

Circulation is the characteristic feature of successful currency systems, from community currencies to cryptocurrencies to national currencies. In this paper, we propose a network analysis approach especially suited for studying circulation given a system's digital transaction records. Sarafu is a digital community currency that was active in Kenya over a period that saw considerable economic disruption due to the COVID-19 pandemic. We represent its circulation as a network of monetary flow among the 40,000 Sarafu users. Network flow analysis reveals that circulation was highly modular, geographically localized, and occurring among users with diverse livelihoods. Across localized sub-populations, network cycle analysis supports the intuitive notion that circulation requires cycles. Moreover, the sub-networks underlying circulation are consistently degree disassortative and we find evidence of preferential attachment. Community-based institutions often take on the role of local hubs, and network centrality measures confirm the importance of early adopters and of women's participation. This work demonstrates that networks of monetary flow enable the study of circulation within currency systems at a striking level of detail, and our findings can be used to inform the development of community currencies in marginalized areas.

The effects of hemodialysis on the functional brain connectivity in patients with end-stage renal disease with functional near-infrared spectroscopy

This study aimed to investigate functional brain connectivity in patients with end-stage renal disease (ESRD) undergoing hemodialysis using functional near-infrared spectroscopy (fNIRS) and to analyze the effect of hemodialysis on functional brain connectivity. We prospectively enrolled patients with ESRD undergoing hemodialysis for > 6 months without any history of neurological or psychiatric disorders. fNIRS data were acquired using a NIRSIT Lite device. Measurements were performed thrice in the resting state for each patient: before the start of hemodialysis (pre-HD), 1 h after the start of hemodialysis (mid-HD), and after the end of hemodialysis (post-HD). We processed and exported all data, and created a weighted connectivity matrix using Pearson correlation analysis. We obtained functional connectivity measures from the connectivity matrix by applying a graph theoretical analysis. We then compared differences in functional connectivity measures according to hemodialysis status in patients with ESRD. We included 34 patients with ESRD. There were significant changes in the mean clustering coefficient, transitivity, and assortative coefficient between the pre- and post-HD periods (0.353 vs. 0.399, p = 0.047; 0.523 vs. 0.600, p = 0.042; and 0.043 vs. - 0.012, p = 0.044, respectively). However, there were no changes in the mean clustering coefficient, transitivity, and assortative coefficient between the pre- and mid-HD periods, or between the mid- and post-HD periods. In addition, there were no significant differences in the average strength, global efficiency, and local efficiency among the pre-, mid-, and post-HD periods. We demonstrated a significant effect of hemodialysis on functional brain connectivity in patients with ESRD. Functional brain connectivity changes more efficiently during hemodialysis.

Gender-based homophily in collaborations across a heterogeneous scholarly landscape

In this article, we investigate the role of gender in collaboration patterns by analyzing gender-based homophily-the tendency for researchers to co-author with individuals of the same gender. We develop and apply novel methodology to the corpus of JSTOR articles, a broad scholarly landscape, which we analyze at various levels of granularity. Most notably, for a precise analysis of gender homophily, we develop methodology which explicitly accounts for the fact that the data comprises heterogeneous intellectual communities and that not all authorships are exchangeable. In particular, we distinguish three phenomena which may affect the distribution of observed gender homophily in collaborations: a structural component that is due to demographics and non-gendered authorship norms of a scholarly community, a compositional component which is driven by varying gender representation across sub-disciplines and time, and a behavioral component which we define as the remainder of observed gender homophily after its structural and compositional components have been taken into account. Using minimal modeling assumptions, the methodology we develop allows us to test for behavioral homophily. We find that statistically significant behavioral homophily can be detected across the JSTOR corpus and show that this finding is robust to missing gender indicators in our data. In a secondary analysis, we show that the proportion of women representation in a field is positively associated with the probability of finding statistically significant behavioral homophily.

Complex network of eye movements during rapid automatized naming

Introduction

Although the method of visualizing eye-tracking data as a time-series might enhance performance in the understanding of gaze behavior, it has not yet been thoroughly examined in the context of rapid automated naming (RAN).

Methods

This study attempted, for the first time, to measure gaze behavior during RAN from the perspective of network-domain, which constructed a complex network [referred to as gaze-time-series-based complex network (GCN)] from gaze time-series. Hence, without designating regions of interest, the features of gaze behavior during RAN were extracted by computing topological parameters of GCN. A sample of 98 children (52 males, aged 11.50 ± 0.28 years) was studied. Nine topological parameters (i.e., average degree, network diameter, characteristic path length, clustering coefficient, global efficiency, assortativity coefficient, modularity, community number, and small-worldness) were computed.

Results

Findings showed that GCN in each RAN task was assortative and possessed “small-world” and community architecture. Additionally, observations regarding the influence of RAN task types included that: (i) five topological parameters (i.e., average degree, clustering coefficient, assortativity coefficient, modularity, and community number) could reflect the difference between tasks N-num (i.e., naming of numbers) and N-cha (i.e., naming of Chinese characters); (ii) there was only one topological parameter (i.e., network diameter) which could reflect the difference between tasks N-obj (i.e., naming of objects) and N-col (i.e., naming of colors); and (iii) when compared to GCN in alphanumeric RAN, GCN in non-alphanumeric RAN may have higher average degree, global efficiency, and small-worldness, but lower network diameter, characteristic path length, clustering coefficient, and modularity. Findings also illustrated that most of these topological parameters were largely independent of traditional eye-movement metrics.

Discussion

This article revealed the architecture and topological parameters of GCN as well as the influence of task types on them, and thus brought some new insights into the understanding of RAN from the perspective of complex network.

Alterations of the thalamic nuclei volumes and intrinsic thalamic network in patients with restless legs syndrome

We aimed to investigate the alterations of thalamic nuclei volumes and intrinsic thalamic network in patients with primary restless legs syndrome (RLS) compared to healthy controls. Seventy-one patients with primary RLS and 55 healthy controls were recruited. They underwent brain MRI using a three-tesla MRI scanner, including three-dimensional T1-weighted images. The intrinsic thalamic network was determined using graph theoretical analysis. The right and left whole thalamic volumes, and the right pulvinar inferior, left ventral posterolateral, left medial ventral, and left pulvinar inferior nuclei volumes in the patients with RLS were lower than those in healthy controls (0.433 vs. 0.447%, p = 0.034; 0.482 vs. 0.502%, p = 0.016; 0.013 vs. 0.015%, p = 0.031; 0.062 vs. 0.065%, p = 0.035; 0.001 vs. 0.001%, p = 0.034; 0.018 vs. 0.020%, p = 0.043; respectively). There was also a difference in the intrinsic thalamic network between the groups. The assortative coefficient in patients with RLS was higher than that in healthy controls (0.0318 vs. - 0.0358, p = 0.048). We demonstrated the alterations of thalamic nuclei volumes and intrinsic thalamic network in patients with RLS compared to healthy controls. These changes might be related to RLS pathophysiology and suggest the pivotal role of the thalamus in RLS symptoms.

Social association predicts immunological similarity in rewilded mice

Environmental influences on immune phenotypes are well-documented, but our understanding of which elements of the environment affect immune systems, and how, remains vague. Behaviors, including socializing with others, are central to an individual's interaction with its environment. We tracked behavior of rewilded laboratory mice of three inbred strains in outdoor enclosures and examined contributions of behavior, including social associations, to immune phenotypes. We found that the more associated two individuals were, the more similar their immune phenotypes were. Social association was particularly predictive of similar memory T and B cell profiles and was more influential than sibling relationships or worm infection status. These results highlight the importance of social networks for immune phenotype and reveal important immunological correlates of social life.

Using Network Science and Psycholinguistic Megastudies to Examine the Dimensions of Phonological Similarity

Network science was used to examine different dimensions of phonological similarity in English. Data from a phonological associate task and an identification of words in noise task were used to create a phonological association network and a misperception network. These networks were compared to a network formed by a computational metric widely used to assess phonological similarity (i.e., one-phoneme metric). The phonological association network and the misperception network were topographically more similar to each other than either were to the one-phoneme metric network, but there were several network features in common between the one-phoneme metric network and the phonological association network. To assess the influence of network structure on processing, we compared the influence of degree (i.e., neighborhood density) from each of the networks on visual and auditory lexical decision reaction times obtained from two psycholinguistic megastudies. The effect of degree differed across network types and tasks. We discuss the use of each approach to determine phonological similarity and a possible direction forward for language research through the use of multiplex networks.

Quantifying ideological polarization on a network using generalized Euclidean distance

An intensely debated topic is whether political polarization on social media is on the rise. We can investigate this question only if we can quantify polarization, by taking into account how extreme the opinions of the people are, how much they organize into echo chambers, and how these echo chambers organize in the network. Current polarization estimates are insensitive to at least one of these factors: They cannot conclusively clarify the opening question. Here, we propose a measure of ideological polarization that can capture the factors we listed. The measure is based on the generalized Euclidean distance, which estimates the distance between two vectors on a network, e.g., representing people's opinion. This measure can fill the methodological gap left by the state of the art and leads to useful insights when applied to real-world debates happening on social media and to data from the U.S. Congress.

Habitats Within the Plant Root Differ in Bacterial Network Topology and Taxonomic Assortativity

The root microbiome is composed of distinct epiphytic (rhizosphere) and endophytic (endosphere) habitats. Differences in abiotic and biotic factors drive differences in microbial community diversity and composition between these habitats, though how they shape the interactions among community members is unknown. Here, we coupled a large-scale characterization of the rhizosphere and endosphere bacterial communities of 30 plant species across two watering treatments with co-occurrence network analysis to understand how root habitats and soil moisture shape root bacterial network properties. We used a novel bootstrapping procedure and null network modeling to overcome some of the limitations associated with microbial co-occurrence network construction and analysis. Endosphere networks had elevated node betweenness centrality versus the rhizosphere, indicating greater overall connectivity among core bacterial members of the root endosphere. Taxonomic assortativity was higher in the endosphere, whereby positive co-occurrence was more likely between bacteria within the same phylum while negative co-occurrence was more likely between bacterial taxa from different phyla. This taxonomic assortativity could be driven by positive and negative interactions among members of the same or different phylum, respectively, or by similar niche preferences associated with phylum rank among root inhabiting bacteria across plant host species. In contrast to the large differences between root habitats, drought had limited effects on network properties but did result in a higher proportion of shared co-occurrences between rhizosphere and endosphere networks. Our study points to fundamentally different ecological processes shaping bacterial co-occurrence across root habitats. [Formula: see text] Copyright © 2023 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license.

Adaptive and pathological connectivity responses in Parkinson's disease brain networks

Functional imaging has been used extensively to identify and validate disease-specific networks as biomarkers in neurodegenerative disorders. It is not known, however, whether the connectivity patterns in these networks differ with disease progression compared to the beneficial adaptations that may also occur over time. To distinguish the 2 responses, we focused on assortativity, the tendency for network connections to link nodes with similar properties. High assortativity is associated with unstable, inefficient flow through the network. Low assortativity, by contrast, involves more diverse connections that are also more robust and efficient. We found that in Parkinson's disease (PD), network assortativity increased over time. Assoratitivty was high in clinically aggressive genetic variants but was low for genes associated with slow progression. Dopaminergic treatment increased assortativity despite improving motor symptoms, but subthalamic gene therapy, which remodels PD networks, reduced this measure compared to sham surgery. Stereotyped changes in connectivity patterns underlie disease progression and treatment responses in PD networks.

A Network-Based Approach for Improving Annotation of Transcription Factor Functions and Binding Sites in Arabidopsis thaliana

Transcription factors are an integral component of the cellular machinery responsible for regulating many biological processes, and they recognize distinct DNA sequence patterns as well as internal/external signals to mediate target gene expression. The functional roles of an individual transcription factor can be traced back to the functions of its target genes. While such functional associations can be inferred through the use of binding evidence from high-throughput sequencing technologies available today, including chromatin immunoprecipitation sequencing, such experiments can be resource-consuming. On the other hand, exploratory analysis driven by computational techniques can alleviate this burden by narrowing the search scope, but the results are often deemed low-quality or non-specific by biologists. In this paper, we introduce a data-driven, statistics-based strategy to predict novel functional associations for transcription factors in the model plant Arabidopsis thaliana. To achieve this, we leverage one of the largest available gene expression compendia to build a genome-wide transcriptional regulatory network and infer regulatory relationships among transcription factors and their targets. We then use this network to build a pool of likely downstream targets for each transcription factor and query each target pool for functionally enriched gene ontology terms. The results exhibited sufficient statistical significance to annotate most of the transcription factors in Arabidopsis with highly specific biological processes. We also perform DNA binding motif discovery for transcription factors based on their target pool. We show that the predicted functions and motifs strongly agree with curated databases constructed from experimental evidence. In addition, statistical analysis of the network revealed interesting patterns and connections between network topology and system-level transcriptional regulation properties. We believe that the methods demonstrated in this work can be extended to other species to improve the annotation of transcription factors and understand transcriptional regulation on a system level.

Understanding dynamics of polarization via multiagent social simulation

It is widely recognized that the Web contributes to user polarization, and such polarization affects not just politics but also peoples' stances about public health, such as vaccination. Understanding polarization in social networks is challenging because it depends not only on user attitudes but also their interactions and exposure to information. We adopt Social Judgment Theory to operationalize attitude shift and model user behavior based on empirical evidence from past studies. We design a social simulation to analyze how content sharing affects user satisfaction and polarization in a social network. We investigate the influence of varying tolerance in users and selectively exposing users to congenial views. We find that (1) higher user tolerance slows down polarization and leads to lower user satisfaction; (2) higher selective exposure leads to higher polarization and lower user reach; and (3) both higher tolerance and higher selective exposure lead to a more homophilic social network.

Cohesion and segregation in the value migration network: Evidence from network partitioning based on sector classification and clustering

Cluster structure detection of the network is a basic problem of complex network analysis. This study investigates the structure of the value migration network using data from 499 stocks listed in the S&P500 as of the end of 2021. An examination is carried out whether the process of value migration creates a cluster structure in the network of companies according to economic activity. Specifically, the cohesion and segregation of the extracted modules in the network division according to (i) sector classification, (ii) community division, and (iii) network clustering decomposition are assessed. The results of this study show that the sector classification of the value migration network has a non-cohesive structure, which means that the flow of value in the financial market occurs between companies from various industries. Moreover, the divisions of the value migration network based on community detection and clustering algorithm are characterized by intra-cluster similarity between the vertices and have a strong community structure. The structure of the network division into modules corresponding to the classification of economic sectors differs significantly from the partition based on the algorithms applied.

Combinatorial characterizations and impossibilities for higher-order homophily

Homophily is the seemingly ubiquitous tendency for people to connect and interact with other individuals who are similar to them. This is a well-documented principle and is fundamental for how society organizes. Although many social interactions occur in groups, homophily has traditionally been measured using a graph model, which only accounts for pairwise interactions involving two individuals. Here, we develop a framework using hypergraphs to quantify homophily from group interactions. This reveals natural patterns of group homophily that appear with gender in scientific collaboration and political affiliation in legislative bill cosponsorship and also reveals distinctive gender distributions in group photographs, all of which cannot be fully captured by pairwise measures. At the same time, we show that seemingly natural ways to define group homophily are combinatorially impossible. This reveals important pitfalls to avoid when defining and interpreting notions of group homophily, as higher-order homophily patterns are governed by combinatorial constraints that are independent of human behavior but are easily overlooked.

Topological dissimilarities of hierarchical resting networks in type 2 diabetes mellitus and obesity

Type 2 diabetes mellitus (T2DM) is reported to cause widespread changes in brain function, leading to cognitive impairments. Research using resting-state functional magnetic resonance imaging data already aims to understand functional changes in complex brain connectivity systems. However, no previous studies with dynamic causal modelling (DCM) tried to investigate large-scale effective connectivity in diabetes. We aimed to examine the differences in large-scale resting state networks in diabetic and obese patients using combined DCM and graph theory methodologies. With the participation of 70 subjects (43 diabetics, 27 obese), we used cross-spectra DCM to estimate connectivity between 36 regions, subdivided into seven resting networks (RSN) commonly recognized in the literature. We assessed group-wise connectivity of T2DM and obesity, as well as group differences, with parametric empirical Bayes and Bayesian model reduction techniques. We analyzed network connectivity globally, between RSNs, and regionally. We found that average connection strength was higher in T2DM globally and between RSNs, as well. On the network level, the salience network shows stronger total within-network connectivity in diabetes (8.07) than in the obese group (4.02). Regionally, we measured the most significant average decrease in the right middle temporal gyrus (-0.013 Hz) and the right inferior parietal lobule (-0.01 Hz) relative to the obese group. In comparison, connectivity increased most notably in the left anterior prefrontal cortex (0.01 Hz) and the medial dorsal thalamus (0.009 Hz). In conclusion, we find the usage of complex analysis of large-scale networks suitable for diabetes instead of focusing on specific changes in brain function.

Reciprocity and interaction effectiveness in generalised mutualisms among free-living species

Mutualistic interactions among free-living species generally involve low-frequency interactions and highly asymmetric dependence among partners, yet our understanding of factors behind their emergence is still limited. Using individual-based interactions of a super-generalist fleshy-fruited plant with its frugivore assemblage, we estimated the Resource Provisioning Effectiveness (RPE) and Seed Dispersal Effectiveness (SDE) to assess the balance in the exchange of resources. Plants were highly dependent on a few frugivore species, while frugivores interacted with most individual plants, resulting in strong asymmetries of mutual dependence. Interaction effectiveness was mainly driven by interaction frequency. Despite highly asymmetric dependences, the strong reliance on quantity of fruit consumed determined high reciprocity in rewards between partners (i.e. higher energy provided by the plant, more seedlings recruited), which was not obscured by minor variations in the quality of animal or plant service. We anticipate reciprocity will emerge in low-intimacy mutualisms where the mutualistic outcome largely relies upon interaction frequency.

Inner composition alignment networks reveal financial impacts of COVID-19

We show that inner composition alignment networks derived for financial time-series data, studied in response to worldwide lockdown imposed in response to COVID-19 situation, show distinct patterns before, during and after lockdown phase. It is observed that significant couplings between companies as captured by inner composition alignment between time series, reduced considerably across the globe during lockdown and post-lockdown recovery period. The study of global community structure of the networks show that factions of companies emerge during recovery phase, with strong coupling within the members of the faction group, a trend which was absent before lockdown period. The study of strongly connected components of the networks further show that market has fragmented in response to COVID-19 situation. We find that most central firms as characterized by in-degree, out-degree and betweenness centralities belong to Chinese and Japanese economies, indicating a role played by these organizations in financial information propagation across the globe. We further observe that recovery phase of the lockdown period is strongly influenced by financial sector, which is one of the main result of this study. It is also observed that two different group of companies, which may not be co-moving, emerge across economies during COVID-19. We further notice that many companies in US and European economy tend to shield themselves from local influences.

Projecting social contact matrices to populations stratified by binary attributes with known homophily

Contact networks are heterogeneous. People with similar characteristics are more likely to interact, a phenomenon called assortative mixing or homophily. Empirical age-stratified social contact matrices have been derived by extensive survey work. We lack however similar empirical studies that provide social contact matrices for a population stratified by attributes beyond age, such as gender, sexual orientation, or ethnicity. Accounting for heterogeneities with respect to these attributes can have a profound effect on model dynamics. Here, we introduce a new method, which uses linear algebra and non-linear optimization, to expand a given contact matrix to populations stratified by binary attributes with a known level of homophily. Using a standard epidemiological model, we highlight the effect homophily can have on model dynamics, and conclude by briefly describing more complicated extensions. The available Python source code enables any modeler to account for the presence of homophily with respect to binary attributes in contact patterns, ultimately yielding more accurate predictive models.

Social stratification in networks: insights from co-authorship networks

It has been observed that real-world social networks often exhibit stratification along economic or other lines, with consequences for class mobility and access to opportunities. With the rise in human interaction data and extensive use of online social networks, the structure of social networks (representing connections between individuals) can be used for measuring stratification. However, although stratification has been studied extensively in the social sciences, there is no single, generally applicable metric for measuring the level of stratification in a network. In this work, we first propose the novel Stratification Assortativity (StA) metric, which measures the extent to which a network is stratified into different tiers. Then, we use the StA metric to perform an in-depth analysis of the stratification of five co-authorship networks. We examine the evolution of these networks over 50 years and show that these fields demonstrate an increasing level of stratification over time, and, correspondingly, the trajectory of a researcher's career is increasingly correlated with her entry point into the network.