Locating influential nodes via dynamics-sensitive centrality

Deciphering population-level response under spatial drug heterogeneity on microhabitat structures

Bacteria and cancer cells live in a spatially heterogeneous environment, where migration shapes the microhabitat structures critical for colonization and metastasis. The interplay between growth, migration, and microhabitat structure complicates the prediction of population responses to drugs, such as clearance or sustained growth, posing a longstanding challenge. Here, we disentangle growth-migration dynamics and identify that population decline is determined by two decoupled terms: a spatial growth variation term and a microhabitat structure term. Notably, the microhabitat structure term can be interpreted as a dynamic-related centrality measure. For fixed spatial drug arrangements, we show that interpreting these centralities reveals how different network structures, even with identical edge densities, microhabitat numbers, and spatial heterogeneity, can lead to distinct population-level responses. Increasing edge density shifts the population response from growth to clearance, supporting an inversed centrality-connectivity relationship, and mirroring the effects of higher migration rates. Furthermore, we derive a sufficient condition for robust population decline across various spatial growth rate arrangements, regardless of spatial-temporal fluctuations induced by drugs. Additionally, we demonstrate that varying the maximum growth-to-death ratio, determined by drug-bacteria interactions, can lead to distinct population decline profiles and a minimal decline phase emerges. These findings address key challenges in predicting population-level responses and provide insights into divergent clinical outcomes under identical drug dosages. This work may offer a new method of interpreting treatment dynamics and potential approaches for optimizing spatially explicit drug dosing strategies.

Allostery in Protein Tyrosine Phosphatases is Enabled by Divergent Dynamics

Dynamics-driven allostery provides important insights into the working mechanics of proteins, especially enzymes. In this study, we employ this paradigm to answer a basic question: in enzyme superfamilies, where the catalytic mechanism, active sites, and protein fold are conserved, what accounts for the difference in the catalytic prowess of the individual members? We show that when subtle changes in sequence do not translate to changes in structure, they do translate to changes in dynamics. We use sequentially diverse PTP1B, TbPTP1, and YopH as representatives of the conserved protein tyrosine phosphatase (PTP) superfamily. Using amino acid network analysis of group behavior (community analysis) and influential node dominance on networks (eigenvector centrality), we explain the dynamic basis of the catalytic variations seen between the three proteins. Importantly, we explain how a dynamics-based blueprint makes PTP1B amenable to allosteric control and how the same is abstracted in TbPTP1 and YopH.

A new causal centrality measure reveals the prominent role of subcortical structures in the causal architecture of the extended default mode network

Network representation has been an incredibly useful concept for understanding the behavior of complex systems in social sciences, biology, neuroscience, and beyond. Network science is mathematically founded on graph theory, where nodal importance is gauged using measures of centrality. Notably, recent work suggests that the topological centrality of a node should not be over-interpreted as its dynamical or causal importance in the network. Hence, identifying the influential nodes in dynamic causal models (DCM) remains an open question. This paper introduces causal centrality for DCM, a dynamics-sensitive and causally-founded centrality measure based on the notion of intervention in graphical models. Operationally, this measure simplifies to an identifiable expression using Bayesian model reduction. As a proof of concept, the average DCM of the extended default mode network (eDMN) was computed in 74 healthy subjects. Next, causal centralities of different regions were computed for this causal graph, and compared against several graph-theoretical centralities. The results showed that the subcortical structures of the eDMN were more causally central than the cortical regions, even though the graph-theoretical centralities unanimously favored the latter. Importantly, model comparison revealed that only the pattern of causal centrality was causally relevant. These results are consistent with the crucial role of the subcortical structures in the neuromodulatory systems of the brain, and highlight their contribution to the organization of large-scale networks. Potential applications of causal centrality-to study causal models of other neurotypical and pathological functional networks-are discussed, and some future lines of research are outlined.

Allostery in Protein Tyrosine Phosphatases is Enabled by Divergent Dynamics

Dynamics-driven allostery provides important insights into the working mechanics of proteins, especially enzymes. In this study we employ this paradigm to answer a basic question: in enzyme superfamilies where the catalytic mechanism, active sites and protein fold are conserved, what accounts for the difference in the catalytic prowess of the individual members? We show that when subtle changes in sequence do not translate to changes in structure, they do translate to changes in dynamics. We use sequentially diverse PTP1B, TbPTP1, and YopH as the representatives of the conserved Protein Tyrosine Phosphatase (PTP) superfamily. Using amino acid network analysis of group behavior (community analysis) and influential node dominance on networks (eigenvector centrality), we explain the dynamic basis of catalytic variations seen between the three proteins. Importantly, we explain how a dynamics-based blueprint makes PTP1B amenable to allosteric control and how the same is abstracted in TbPTP1 and YopH.

Identifying spreading influence nodes for social networks

The identification of spreading influence nodes in social networks, which studies how to detect important individuals in human society, has attracted increasing attention from physical and computer science, social science and economics communities. The identification algorithms of spreading influence nodes can be used to evaluate the spreading influence, describe the node’s position, and identify interaction centralities. This review summarizes the recent progress about the identification algorithms of spreading influence nodes from the viewpoint of social networks, emphasizing the contributions from physical perspectives and approaches, including the microstructure-based algorithms, community structure-based algorithms, macrostructure-based algorithms, and machine learning-based algorithms. We introduce diffusion models and performance evaluation metrics, and outline future challenges of the identification of spreading influence nodes.

A Temporal Network Model for Livestock Trade Systems

The movements of animals between farms and other livestock holdings for trading activities form a complex livestock trade network. These movements play an important role in the spread of infectious diseases among premises. For studying the disease spreading among animal holdings, it is of great importance to understand the structure and dynamics of the trade system. In this paper, we propose a temporal network model for animal trade systems. Furthermore, a novel measure of node centrality important for disease spreading is introduced. The experimental results show that the model can reasonably well describe these spreading-related properties of the network and it can generate crucial data for research in the field of the livestock trade system.

Identification of influencers in online social networks: measuring influence considering multidimensional factors exploration

Online Social networks exhibit heterogeneous nature with nodes playing far different roles in structure and function. To identify influencers is thus very significant, allowing us to control the outbreak of public negative opinion, to conduct advertisements for e-commercial products, to predict popular scientific publications, and so on. The identification of influencers attracts increasing attentions from both computer science and communication science, with multiple dimensional metrics ranging from structure-based to information-based and action-based. However, most work simply rely on one dimensional metrics. Therefore, in this paper, we analyze three dimensional characteristics (structure-based, information-based, and action-based factors) to develop the multidimensional social influence (MSI) measurement approach. With topic distillation and conditional expectation, the MSI approach can not only measure users topic-level influence, but also measure users global-level influence. Based on data collected from SinaWeibo.com, the experimental results show that the proposed framework outperforms two traditional methods (LeaderRank and FBI) both on the topic-level and the global-level. The proposed framework can be effectively applied to promote word-of-mouth marketing, and to steer public opinion in certain directions, even to support decisions during a negotiation process.

Connectivity, reproduction number, and mobility interact to determine communities' epidemiological superspreader potential in a metapopulation network

Disease epidemic outbreaks on human metapopulation networks are often driven by a small number of superspreader nodes, which are primarily responsible for spreading the disease throughout the network. Superspreader nodes typically are characterized either by their locations within the network, by their degree of connectivity and centrality, or by their habitat suitability for the disease, described by their reproduction number (R). Here we introduce a model that considers simultaneously the effects of network properties and R on superspreaders, as opposed to previous research which considered each factor separately. This type of model is applicable to diseases for which habitat suitability varies by climate or land cover, and for direct transmitted diseases for which population density and mitigation practices influences R. We present analytical models that quantify the superspreader capacity of a population node by two measures: probability-dependent superspreader capacity, the expected number of neighboring nodes to which the node in consideration will randomly spread the disease per epidemic generation, and time-dependent superspreader capacity, the rate at which the node spreads the disease to each of its neighbors. We validate our analytical models with a Monte Carlo analysis of repeated stochastic Susceptible-Infected-Recovered (SIR) simulations on randomly generated human population networks, and we use a random forest statistical model to relate superspreader risk to connectivity, R, centrality, clustering, and diffusion. We demonstrate that either degree of connectivity or R above a certain threshold are sufficient conditions for a node to have a moderate superspreader risk factor, but both are necessary for a node to have a high-risk factor. The statistical model presented in this article can be used to predict the location of superspreader events in future epidemics, and to predict the effectiveness of mitigation strategies that seek to reduce the value of R, alter host movements, or both.

Identifying critical nodes in temporal networks by network embedding

Critical nodes in temporal networks play more significant role than other nodes on the structure and function of networks. The research on identifying critical nodes in temporal networks has attracted much attention since the real-world systems can be illustrated more accurately by temporal networks than static networks. Considering the topological information of networks, the algorithm MLI based on network embedding and machine learning are proposed in this paper. we convert the critical node identification problem in temporal networks into regression problem by the algorithm. The effectiveness of proposed methods is evaluated by SIR model and compared with well-known existing metrics such as temporal versions of betweenness, closeness, k-shell, degree deviation and dynamics-sensitive centralities in one synthetic and five real temporal networks. Experimental results show that the proposed method outperform these well-known methods in identifying critical nodes under spreading dynamic.

Identifying vital nodes in complex networks by adjacency information entropy

Identifying the vital nodes in networks is of great significance for understanding the function of nodes and the nature of networks. Many centrality indices, such as betweenness centrality (BC), eccentricity centrality (EC), closeness centricity (CC), structural holes (SH), degree centrality (DC), PageRank (PR) and eigenvector centrality (VC), have been proposed to identify the influential nodes of networks. However, some of these indices have limited application scopes. EC and CC are generally only applicable to undirected networks, while PR and VC are generally used for directed networks. To design a more applicable centrality measure, two vital node identification algorithms based on node adjacency information entropy are proposed in this paper. To validate the effectiveness and applicability of the proposed algorithms, contrast experiments are conducted with the BC, EC, CC, SH, DC, PR and VC indices in different kinds of networks. The results show that the index in this paper has a high correlation with the local metric DC, and it also has a certain correlation with the PR and VC indices for directed networks. In addition, the experimental results indicate that our algorithms can effectively identify the vital nodes in different networks.

Identifying Influential Nodes in Complex Networks Based on Local Effective Distance

With the rapid development of Internet technology, the social network has gradually become an indispensable platform for users to release information, obtain information, and share information. Users are not only receivers of information, but also publishers and disseminators of information. How to select a certain number of users to use their influence to achieve the maximum dissemination of information has become a hot topic at home and abroad. Rapid and accurate identification of influential nodes in the network is of great practical significance, such as the rapid dissemination, suppression of social network information, and the smooth operation of the network. Therefore, from the perspective of improving computational accuracy and efficiency, we propose an influential node identification method based on effective distance, named KDEC. By quantifying the effective distance between nodes and combining the position of the node in the network and its local structure, the influence of the node in the network is obtained, which is used as an indicator to evaluate the influence of the node. Through experimental analysis of a lot of real-world networks, the results show that the method can quickly and accurately identify the influential nodes in the network, and is better than some classical algorithms and some recently proposed algorithms.

Identifying influential spreaders by gravity model

Identifying influential spreaders in complex networks is crucial in understanding, controlling and accelerating spreading processes for diseases, information, innovations, behaviors, and so on. Inspired by the gravity law, we propose a gravity model that utilizes both neighborhood information and path information to measure a node's importance in spreading dynamics. In order to reduce the accumulated errors caused by interactions at distance and to lower the computational complexity, a local version of the gravity model is further proposed by introducing a truncation radius. Empirical analyses of the Susceptible-Infected-Recovered (SIR) spreading dynamics on fourteen real networks show that the gravity model and the local gravity model perform very competitively in comparison with well-known state-of-the-art methods. For the local gravity model, the empirical results suggest an approximately linear relation between the optimal truncation radius and the average distance of the network.

Maximizing Network Resilience against Malicious Attacks

The threat of a malicious attack is one of the major security problems in complex networks. Resilience is the system-level self-adjusting ability of a complex network to retain its basic functionality and recover rapidly from major disruptions. Despite numerous heuristic enhancement methods, there is a research gap in maximizing network resilience: current heuristic methods are designed to immunize vital nodes or modify a network to a specific onion-like structure and cannot maximize resilience theoretically via network structure. Here we map complex networks onto a physical elastic system to introduce indices of network resilience, and propose a unified theoretical framework and general approach, which can address the optimal problem of network resilience by slightly modifying network structures (i.e., by adding a set of structural edges). We demonstrate the high efficiency of this approach on three realistic networks as well as two artificial random networks. Case studies show that the proposed approach can maximize the resilience of complex networks while maintaining their topological functionality. This approach helps to unveil hitherto hidden functions of some inconspicuous components, which in turn, can be used to guide the design of resilient systems, offer an effective and efficient approach for mitigating malicious attacks, and furnish self-healing to reconstruct failed infrastructure systems.

Improving short-term information spreading efficiency in scale-free networks by specifying top large-degree vertices as the initial spreaders

The positive function of initially influential vertices could be exploited to improve spreading efficiency for short-term spreading in scale-free networks. However, the selection of initial spreaders depends on the specific scenes. The selection of initial spreaders needs to offer low complexity and low power consumption for short-term spreading. In this paper, we propose a selection strategy for efficiently spreading information by specifying a set of top large-degree vertices as the initially informed vertices. The essential idea behind the proposed selection strategy is to exploit the significant diffusion of the top large-degree vertices at the beginning of spreading. To evaluate the positive impact of initially influential vertices, we first build an information spreading model in the Barabási-Albert (BA) scale-free network; next, we design 54 comparative Monte Carlo experiments based on a benchmark strategy and the proposed selection strategy in different BA scale-free network structures. Experimental results indicate that (i) the proposed selection strategy can significantly improve spreading efficiency in the short-term spreading and (ii) both network size and number of hubs have a strong impact on spreading efficiency, while the number of initially informed vertices has a weak impact. The proposed selection strategy can be employed in short-term spreading, such as sending warnings or crisis information spreading or information spreading in emergency training or realistic emergency scenes.

Dismantling efficiency and network fractality

In network dismantling, a minimal set of nodes is identified whose removal breaks the network into small components of subextensive size. Because finding the optimal set of nodes is an NP-hard problem, several heuristic algorithms have been developed as alternative methods, for instance, the so-called belief propagation-based decimation (BPD) algorithm and the collective influence (CI) algorithm. Here, we test the performance of these algorithms and analyze them in terms of the fractality of the network. Networks are classified into two types: fractal and nonfractal networks. Real-world examples include the World Wide Web and the Internet at the autonomous system level, respectively. They have different ratios of long-range shortcuts to short-range ones. We find that the BPD algorithm works more efficiently than the CI algorithm no matter whether a network is fractal or not. On the other hand, the CI algorithm works better on nonfractal networks than on fractal networks. We construct diverse fractal and nonfractal model networks by controlling parameters such as the degree exponent, shortcut number, and system size and investigate how the performance of the two algorithms depends on structural features.

Identification of influential spreaders in complex networks using HybridRank algorithm

Identifying the influential spreaders in complex networks is crucial to understand who is responsible for the spreading processes and the influence maximization through networks. Targeting these influential spreaders is significant for designing strategies for accelerating the propagation of information that is useful for various applications, such as viral marketing applications or blocking the diffusion of annoying information (spreading of viruses, rumors, online negative behaviors, and cyberbullying). Existing methods such as local centrality measures like degree centrality are less effective, and global measures like closeness and betweenness centrality could better identify influential spreaders but they have some limitations. In this paper, we propose the HybridRank algorithm using a new hybrid centrality measure for detecting a set of influential spreaders using the topological features of the network. We use the SIR spreading model for simulating the spreading processes in networks to evaluate the performance of our algorithm. Empirical experiments are conducted on real and artificial networks, and the results show that the spreaders identified by our approach are more influential than several benchmarks.

Accurate ranking of influential spreaders in networks based on dynamically asymmetric link weights

We propose an efficient and accurate measure for ranking spreaders and identifying the influential ones in spreading processes in networks. While the edges determine the connections among the nodes, their specific role in spreading should be considered explicitly. An edge connecting nodes i and j may differ in its importance for spreading from i to j and from j to i. The key issue is whether node j, after infected by i through the edge, would reach out to other nodes that i itself could not reach directly. It becomes necessary to invoke two unequal weights w_{ij} and w_{ji} characterizing the importance of an edge according to the neighborhoods of nodes i and j. The total asymmetric directional weights originating from a node leads to a novel measure s_{i}, which quantifies the impact of the node in spreading processes. An s-shell decomposition scheme further assigns an s-shell index or weighted coreness to the nodes. The effectiveness and accuracy of rankings based on s_{i} and the weighted coreness are demonstrated by applying them to nine real-world networks. Results show that they generally outperform rankings based on the nodes' degree and k-shell index while maintaining a low computational complexity. Our work represents a crucial step towards understanding and controlling the spread of diseases, rumors, information, trends, and innovations in networks.

Identifying the perceptive users for online social systems

In this paper, the perceptive user, who could identify the high-quality objects in their initial lifespan, is presented. By tracking the ratings given to the rewarded objects, we present a method to identify the user perceptibility, which is defined as the capability that a user can identify these objects at their early lifespan. Moreover, we investigate the behavior patterns of the perceptive users from three dimensions: User activity, correlation characteristics of user rating series and user reputation. The experimental results for the empirical networks indicate that high perceptibility users show significantly different behavior patterns with the others: Having larger degree, stronger correlation of rating series and higher reputation. Furthermore, in view of the hysteresis in finding the rewarded objects, we present a general framework for identifying the high perceptibility users based on user behavior patterns. The experimental results show that this work is helpful for deeply understanding the collective behavior patterns for online users.

Dynamic-Sensitive centrality of nodes in temporal networks

Locating influential nodes in temporal networks has attracted a lot of attention as data driven and diverse applications. Classic works either looked at analysing static networks or placed too much emphasis on the topological information but rarely highlighted the dynamics. In this paper, we take account the network dynamics and extend the concept of Dynamic-Sensitive centrality to temporal network. According to the empirical results on three real-world temporal networks and a theoretical temporal network for susceptible-infected-recovered (SIR) models, the temporal Dynamic-Sensitive centrality (TDC) is more accurate than both static versions and temporal versions of degree, closeness and betweenness centrality. As an application, we also use TDC to analyse the impact of time-order on spreading dynamics, we find that both topological structure and dynamics contribute the impact on the spreading influence of nodes, and the impact of time-order on spreading influence will be stronger when spreading rate b deviated from the epidemic threshold bc, especially for the temporal scale-free networks.

Using LTI Dynamics to Identify the Influential Nodes in a Network

Networks are used for modeling numerous technical, social or biological systems. In order to better understand the system dynamics, it is a matter of great interest to identify the most important nodes within the network. For a large set of problems, whether it is the optimal use of available resources, spreading information efficiently or even protection from malicious attacks, the most important node is the most influential spreader, the one that is capable of propagating information in the shortest time to a large portion of the network. Here we propose the Node Imposed Response (NiR), a measure which accurately evaluates node spreading power. It outperforms betweenness, degree, k-shell and h-index centrality in many cases and shows the similar accuracy to dynamics-sensitive centrality. We utilize the system-theoretic approach considering the network as a Linear Time-Invariant system. By observing the system response we can quantify the importance of each node. In addition, our study provides a robust tool set for various protective strategies.

Leveraging percolation theory to single out influential spreaders in networks

Among the consequences of the disordered interaction topology underlying many social, technological, and biological systems, a particularly important one is that some nodes, just because of their position in the network, may have a disproportionate effect on dynamical processes mediated by the complex interaction pattern. For example, the early adoption of a commercial product by an opinion leader in a social network may change its fate or just a few superspreaders may determine the virality of a meme in social media. Despite many recent efforts, the formulation of an accurate method to optimally identify influential nodes in complex network topologies remains an unsolved challenge. Here, we present the exact solution of the problem for the specific, but highly relevant, case of the susceptible-infected-removed (SIR) model for epidemic spreading at criticality. By exploiting the mapping between bond percolation and the static properties of the SIR model, we prove that the recently introduced nonbacktracking centrality is the optimal criterion for the identification of influential spreaders in locally tree-like networks at criticality. By means of simulations on synthetic networks and on a very extensive set of real-world networks, we show that the nonbacktracking centrality is a highly reliable metric to identify top influential spreaders also in generic graphs not embedded in space and for noncritical spreading.