Local modularity measure for network clusterizations

Multimodal sleep signal tensor decomposition and hidden Markov Modeling for temazepam-induced anomalies across age groups

BACKGROUND

Recent advances in multimodal signal analysis enable the identification of subtle drug-induced anomalies in sleep that traditional methods often miss.

NEW METHOD

We develop and introduce the Dynamic Representation of Multimodal Activity and Markov States (DREAMS) framework, which embeds explainable artificial intelligence (XAI) techniques to model hidden state transitions during sleep using tensorized EEG, EMG, and EOG signals from 22 subjects across three age groups (18-29, 30-49, and 50-66 years). By combining Tucker decomposition with probabilistic Hidden Markov Modeling, we quantified age-specific, temazepam-induced hidden states and significant differences in transition probabilities.

RESULTS

Jensen-Shannon Divergence (JSD) was employed to assess variability in hidden state transitions, with older subjects (50-66 years) under temazepam displaying heightened transition variability and network instability as indicated by a 48.57 % increase in JSD (from 0.35 to 0.52) and reductions in network density by 12.5 % (from 0.48 to 0.42) and modularity by 21.88 % (from 0.32 to 0.25). These changes reflect temazepam's disruptive impact on sleep architecture in older adults, aligning with known age-related declines in sleep stability and pharmacological sensitivity. In contrast, younger subjects exhibited lower divergence and retained relatively stable, cyclical transition patterns. Anomaly scores further quantified deviations in state transitions, with older subjects showing increased transition uncertainty and marked deviations in REM-like to NREM state transitions.

COMPARISON WITH EXISTING METHODS

This XAI-driven framework provides transparent, age-specific insights into temazepam's impact on sleep dynamics, going beyond traditional methods by identifying subtle, pharmacologically induced changes in sleep stage transitions that would otherwise be missed.

CONCLUSIONS

DREAMS supports the development of personalized interventions based on sleep transition variability across age groups, offering a powerful tool to understand temazepam's age-dependent effects on sleep architecture.

Research Hotspots and Development Trends on Apolipoprotein B in the Field of Atherosclerosis: A Bibliometric Analysis

BACKGROUND

Cardiovascular diseases caused by atherosclerosis (AS) are the leading causes of disability and death worldwide. Apolipoprotein B (ApoB), the core protein of low-density lipoproteins, is a major contributor to cardiovascular disease-related morbidity and mortality, with apolipoprotein B (ApoB) playing a critical role in its pathogenesis. However, no bibliometric studies on the involvement of ApoB in AS have been published. This study aimed to conduct a comprehensive bibliometric analysis to explore the current and future trends regarding the role of ApoB in AS.

METHODS

Utilizing the Web of Science Core Collection, a thorough search was conducted for ApoB in AS-related papers related to research on ApoB in the field of AS during 1991-2023. The analysis focused on annual publication trends, leading countries/regions and institutions, influential authors, journal and key journals. CiteSpace and VOSviewer were employed to visualize reference co-citations, and keyword co-occurrences, offering insights into the research landscape and emerging trends.

RESULTS

This bibliometric analysis employed network diagrams for cluster analysis of a total of 2105 articles and reviews, evidencing a discernible upward trend in annual publication volume. This corpus of research emanates from 76 countries/regions and 2343 organizations, illustrating the widespread international engagement in ApoB-related AS studies. Notably, the United States and the University of California emerge as the most prolific contributors, which underscores their pivotal roles in advancing this research domain. The thematic investigation has increasingly focused on elucidating the mechanistic involvement of ApoB in atherosclerosis, its potential as a diagnostic biomarker, and its implications for therapeutic strategies.

CONCLUSION

This bibliometric analysis provides the first comprehensive perspective on the evolving promise of ApoB in AS-related research, emphasizing the importance of this molecule in opening up new diagnostic and therapeutic avenues. This study emphasizes the need for continued research and interdisciplinary efforts to strengthen the fight against AS. Furthermore, it emphasizes the critical role of international collaboration and interdisciplinary exploration in leveraging new insights to achieve clinical breakthroughs, thereby addressing the complexities of AS by focusing on ApoB.

Sleep Profiles in Eating Disorders: A Scientometric Study on 50 Years of Clinical Research

Sleep and diet are essential for maintaining physical and mental health. These two factors are closely intertwined and affect each other in both timing and quality. Eating disorders, including anorexia nervosa and bulimia nervosa, are often accompanied by different sleep problems. In modern society, an increasing number of studies are being conducted on the relationship between eating disorders and sleep. To gain a more comprehensive understanding of this field and highlight influential papers as well as the main research domains in this area, a scientometric approach was used to review 727 publications from 1971 to 2023. All documents were retrieved from Scopus through the following string "TITLE-ABS (("sleep" OR "insomnia") AND ("anorexia nervosa" OR "bulimia nervosa" OR "binge eating" OR "eating disorder*") AND NOT "obes*") AND (LIMIT-TO (LANGUAGE, "English"))". A document co-citation analysis was applied to map the relationship between relevant articles and their cited references as well as the gaps in the literature. Nine publications on sleep and eating disorders were frequently cited, with an article by Vetrugno and colleagues on nocturnal eating being the most impactful in the network. The results also indicated a total of seven major thematic research clusters. The qualitative inspection of clusters strongly highlights the reciprocal influence of disordered eating and sleeping patterns. Researchers have modelled this reciprocal influence by taking into account the role played by pharmacological (e.g., zolpidem, topiramate), hormonal (e.g., ghrelin), and psychological (e.g., anxiety, depression) factors, pharmacological triggers, and treatments for eating disorders and sleep problems. The use of scientometric perspectives provides valuable insights into the field related to sleep and eating disorders, which can guide future research directions and foster a more comprehensive understanding of this important area.

Spatial, temporal and network analyses provide insights into the dynamics of the bacterial communities associated with two species of Caribbean octocorals and indicate possible key taxa

Despite the current decline of scleractinian coral populations, octocorals are thriving on reefs in the Caribbean Sea and western North Atlantic Ocean. These cnidarians are holobiont entities, interacting with a diverse array of microorganisms. Few studies have investigated the spatial and temporal stability of the bacterial communities associated with octocoral species and information regarding the co-occurrence and potential interactions between specific members of these bacterial communities remain sparse. To address this knowledge gap, this study investigated the stability of the bacterial assemblages associated with two common Caribbean octocoral species, Eunicea flexuosa and Antillogorgia americana, across time and geographical locations and performed network analyses to investigate potential bacterial interactions. Results demonstrated that general inferences regarding the spatial and temporal stability of octocoral-associated bacterial communities should not be made, as host-specific characteristics may influence these factors. In addition, network analyses revealed differences in the complexity of the interactions between bacteria among the octocoral species analyzed, while highlighting the presence of genera known to produce bioactive secondary metabolites in both octocorals that may play fundamental roles in structuring the octocoral-associated bacteriome.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13199-023-00923-x.

Global Research Trends of Artificial Intelligence on Histopathological Images: A 20-Year Bibliometric Analysis

Cancer has become a major threat to global health care. With the development of computer science, artificial intelligence (AI) has been widely applied in histopathological images (HI) analysis. This study analyzed the publications of AI in HI from 2001 to 2021 by bibliometrics, exploring the research status and the potential popular directions in the future. A total of 2844 publications from the Web of Science Core Collection were included in the bibliometric analysis. The country/region, institution, author, journal, keyword, and references were analyzed by using VOSviewer and CiteSpace. The results showed that the number of publications has grown rapidly in the last five years. The USA is the most productive and influential country with 937 publications and 23,010 citations, and most of the authors and institutions with higher numbers of publications and citations are from the USA. Keyword analysis showed that breast cancer, prostate cancer, colorectal cancer, and lung cancer are the tumor types of greatest concern. Co-citation analysis showed that classification and nucleus segmentation are the main research directions of AI-based HI studies. Transfer learning and self-supervised learning in HI is on the rise. This study performed the first bibliometric analysis of AI in HI from multiple indicators, providing insights for researchers to identify key cancer types and understand the research trends of AI application in HI.

From communities to protein complexes: A local community detection algorithm on PPI networks

Identifying protein complexes in protein-protein interaction (ppi) networks is often handled as a community detection problem, with algorithms generally relying exclusively on the network topology for discovering a solution. The advancement of experimental techniques on ppi has motivated the generation of many Gene Ontology (go) databases. Incorporating the functionality extracted from go with the topological properties from the underlying ppi network yield a novel approach to identify protein complexes. Additionally, most of the existing algorithms use global measures that operate on the entire network to identify communities. The result of using global metrics are large communities that are often not correlated with the functionality of the proteins. Moreover, ppi network analysis shows that most of the biological functions possibly lie between local neighbours in ppi networks, which are not identifiable with global metrics. In this paper, we propose a local community detection algorithm, (lcda-go), that uniquely exploits information of functionality from go combined with the network topology. lcda-go identifies the community of each protein based on the topological and functional knowledge acquired solely from the local neighbour proteins within the ppi network. Experimental results using the Krogan dataset demonstrate that our algorithm outperforms in most cases state-of-the-art approaches in assessment based on Precision, Sensitivity, and particularly Composite Score. We also deployed lcda, the local-topology based precursor of lcda-go, to compare with a similar state-of-the-art approach that exclusively incorporates topological information of ppi networks for community detection. In addition to the high quality of the results, one main advantage of lcda-go is its low computational time complexity.

Temporal evolution, most influential studies and sleeping beauties of the coronavirus literature

Following the outbreak of SARS-CoV-2 disease, within less than 8 months, the 50 years-old scholarly literature of coronaviruses grew to nearly three times larger than its size prior to 2020. Here, temporal evolution of the coronavirus literature over the last 30 years (N = 43,769) is analysed along with its subdomain of SARS-CoV-2 articles (N = 27,460) and the subdomain of reviews and meta-analytic studies (N = 1027). The analyses are conducted through the lenses of co-citation and bibliographic coupling of documents. (1) Of the N = 1204 review and meta-analytical articles of the coronavirus literature, nearly 88% have been published and indexed during the first 8 months of 2020, marking an unprecedented attention to reviews and meta-analyses in this domain, prompted by the SARS-CoV-2 pandemic. (2) The subset of 2020 SARS-CoV-2 articles is bibliographically distant from the rest of this literature published prior to 2020. Individual articles of the SARS-CoV-2 segment with a bridging role between the two bodies of articles (i.e., before and after 2020) are identifiable. (3) Furthermore, the degree of bibliographic coupling within the 2020 SARS-CoV-2 cluster is much poorer compared to the cluster of articles published prior to 2020. This could, in part, be explained by the higher diversity of topics that are studied in relation to SARS-CoV-2 compared to the literature of coronaviruses published prior to the SARS-CoV-2 disease. (4) The analyses on the subset of SARS-CoV-2 literature identified studies published prior to 2020 that have now proven highly instrumental in the development of various clusters of publications linked to SARS-CoV-2. In particular, the so-called "sleeping beauties" of the coronavirus literature with an awakening in 2020 were identified, i.e., previously published studies of this literature that had remained relatively unnoticed for several years but gained sudden traction in 2020 in the wake of the SARS-CoV-2 outbreak. This work documents the historical development of the literature on coronaviruses as an event-driven literature and as a domain that exhibited, arguably, the most exceptional case of publication burst in the history of science. It also demonstrates how scholarly efforts undertaken during peace time or prior to a disease outbreak could suddenly play a critical role in prevention and mitigation of health disasters caused by new diseases.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11192-021-04036-4.

Revealing shared differential co-expression profiles in rice infected by virus from reoviridae and sequiviridae group

Differential co-expression is a cutting-edge approach to analyze gene expression data and identify both shared and divergent expression patterns. The availability of high-throughput gene expression datasets and efficient computational approaches have unfolded the opportunity to a systems level understanding of functional genomics of different stresses with respect to plants. We performed the meta-analysis of the available microarray data for reoviridae and sequiviridae infection in rice with the aim to identify the shared gene co-expression profile. The microarray data were downloaded from ArrayExpress and analyzed through a modified Weighted Gene Co-expression Network Analysis (WGCNA) protocol. WGCNA clustered the genes based on the expression intensities across the samples followed by identification of modules, eigengenes, principal components, topology overlap, module membership and module preservation. The module preservation analysis identified 4 modules; salmon (638 genes), midnightblue (584 genes), lightcyan (686 genes) and red (562 genes), which are highly preserved in both the cases. The networks in case of reoviridae infection showed neatly packed clusters whereas, in sequiviridae, the clusters were loosely connected which is due to the differences in the correlation values. We also identified 83 common transcription factors targeting the hub genes from all the identified modules. This study provides a coherent view of the comparative aspect of the expression of common genes involved in different virus infections which may aid in the identification of novel targets and development of new intervention strategy against the virus.

Global vs local modularity for network community detection

Community structures are ubiquitous in various complex networks, implying that the networks commonly be composed of groups of nodes with more internal links and less external links. As an important topic in network theory, community detection is of importance for understanding the structure and function of the networks. Optimizing statistical measures for community structures is one of most popular strategies for community detection in complex networks. In the paper, by using a type of self-loop rescaling strategy, we introduced a set of global modularity functions and a set of local modularity functions for community detection in networks, which are optimized by a kind of the self-consistent method. We carefully compared and analyzed the behaviors of the modularity-based methods in community detection, and confirmed the superiority of the local modularity for detecting community structures on large-size and heterogeneous networks. The local modularity can more quickly eliminate the first-type limit of modularity, and can eliminate or alleviate the second-type limit of modularity in networks, because of the use of the local information in networks. Moreover, we tested the methods in real networks. Finally, we expect the research can provide useful insight into the problem of community detection in complex networks.

Feature Subset Selection for Cancer Classification Using Weight Local Modularity

Microarray is recently becoming an important tool for profiling the global gene expression patterns of tissues. Gene selection is a popular technology for cancer classification that aims to identify a small number of informative genes from thousands of genes that may contribute to the occurrence of cancers to obtain a high predictive accuracy. This technique has been extensively studied in recent years. This study develops a novel feature selection (FS) method for gene subset selection by utilizing the Weight Local Modularity (WLM) in a complex network, called the WLMGS. In the proposed method, the discriminative power of gene subset is evaluated by using the weight local modularity of a weighted sample graph in the gene subset where the intra-class distance is small and the inter-class distance is large. A higher local modularity of the gene subset corresponds to a greater discriminative of the gene subset. With the use of forward search strategy, a more informative gene subset as a group can be selected for the classification process. Computational experiments show that the proposed algorithm can select a small subset of the predictive gene as a group while preserving classification accuracy.

Unsupervised spatial event detection in targeted domains with applications to civil unrest modeling

Twitter has become a popular data source as a surrogate for monitoring and detecting events. Targeted domains such as crime, election, and social unrest require the creation of algorithms capable of detecting events pertinent to these domains. Due to the unstructured language, short-length messages, dynamics, and heterogeneity typical of Twitter data streams, it is technically difficult and labor-intensive to develop and maintain supervised learning systems. We present a novel unsupervised approach for detecting spatial events in targeted domains and illustrate this approach using one specific domain, viz. civil unrest modeling. Given a targeted domain, we propose a dynamic query expansion algorithm to iteratively expand domain-related terms, and generate a tweet homogeneous graph. An anomaly identification method is utilized to detect spatial events over this graph by jointly maximizing local modularity and spatial scan statistics. Extensive experiments conducted in 10 Latin American countries demonstrate the effectiveness of the proposed approach.

Identifying protein complexes and functional modules--from static PPI networks to dynamic PPI networks

Cellular processes are typically carried out by protein complexes and functional modules. Identifying them plays an important role for our attempt to reveal principles of cellular organizations and functions. In this article, we review computational algorithms for identifying protein complexes and/or functional modules from protein-protein interaction (PPI) networks. We first describe issues and pitfalls when interpreting PPI networks. Then based on types of data used and main ideas involved, we briefly describe protein complex and/or functional module identification algorithms in four categories: (i) those based on topological structures of unweighted PPI networks; (ii) those based on characters of weighted PPI networks; (iii) those based on multiple data integrations; and (iv) those based on dynamic PPI networks. The PPI networks are modelled increasingly precise when integrating more types of data, and the study of protein complexes would benefit by shifting from static to dynamic PPI networks.

Tolerating the community detection resolution limit with edge weighting

Communities of vertices within a giant network such as the World Wide Web are likely to be vastly smaller than the network itself. However, Fortunato and Barthélemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than √L/2 edges, where L is the number of edges in the entire network. This resolution limit leads modularity maximization algorithms to have notoriously poor accuracy on many real networks. Fortunato and Barthélemy's argument can be extended to networks with weighted edges as well, and we derive this corollary argument. We conclude that weighted modularity algorithms may fail to resolve communities with less than √Wε/2 total edge weight, where W is the total edge weight in the network and ε is the maximum weight of an intercommunity edge. If ε is small, then small communities can be resolved. Given a weighted or unweighted network, we describe how to derive new edge weights in order to achieve a low ε, we modify the Clauset, Newman, and Moore (CNM) community detection algorithm to maximize weighted modularity, and we show that the resulting algorithm has greatly improved accuracy. In experiments with an emerging community standard benchmark, we find that our simple CNM variant is competitive with the most accurate community detection methods yet proposed.

Measuring the significance of community structure in complex networks

Many complex systems can be represented as networks, and separating a network into communities could simplify functional analysis considerably. Many approaches have recently been proposed to detect communities, but a method to determine whether the detected communities are significant is still lacking. In this paper, an index to evaluate the significance of communities in networks is proposed based on perturbation of the network. In contrast to previous approaches, the network is disturbed gradually, and the index is defined by integrating all of the similarities between the community structures before and after perturbation. Moreover, by taking the null model into account, the index eliminates scale effects. Thus, it can evaluate and compare the significance of communities in different networks. The method has been tested in many artificial and real-world networks. The results show that the index is in fact independent of the size of the network and the number of communities. With this approach, clear communities are found to always exist in social networks, but significant communities cannot be found in protein interactions and metabolic networks.

Discover protein complexes in protein-protein interaction networks using parametric local modularity

Background

Recent advances in proteomic technologies have enabled us to create detailed protein-protein interaction maps in multiple species and in both normal and diseased cells. As the size of the interaction dataset increases, powerful computational methods are required in order to effectively distil network models from large-scale interactome data.

Results

We present an algorithm, miPALM (Module Inference by Parametric Local Modularity), to infer protein complexes in a protein-protein interaction network. The algorithm uses a novel graph theoretic measure, parametric local modularity, to identify highly connected sub-networks as candidate protein complexes. Using gold standard sets of protein complexes and protein function and localization annotations, we show our algorithm achieved an overall improvement over previous algorithms in terms of precision, recall, and biological relevance of the predicted complexes. We applied our algorithm to predict and characterize a set of 138 novel protein complexes in S. cerevisiae.

Conclusions

miPALM is a novel algorithm for detecting protein complexes from large protein-protein interaction networks with improved accuracy than previous methods. The software is implemented in Matlab and is freely available at http://www.medicine.uiowa.edu/Labs/tan/software.html.

Stability of graph communities across time scales

The complexity of biological, social, and engineering networks makes it desirable to find natural partitions into clusters (or communities) that can provide insight into the structure of the overall system and even act as simplified functional descriptions. Although methods for community detection abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We introduce here the stability of a partition, a measure of its quality as a community structure based on the clustered autocovariance of a dynamic Markov process taking place on the network. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser communities. Our dynamical definition provides a unifying framework for several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler's spectral clustering emerges at long times. We apply our method to characterize the relevance of partitions over time for constructive and real networks, including hierarchical graphs and social networks, and use it to obtain reduced descriptions for atomic-level protein structures over different time scales.

Local resolution-limit-free Potts model for community detection

We report on an exceptionally accurate spin-glass-type Potts model for community detection. With a simple algorithm, we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise. It is also competitive with the best currently available algorithms in terms of speed and size of solvable systems. We find that the computational demand often exhibits superlinear scaling O(L1.3) where L is the number of edges in the system, and we have applied the algorithm to synthetic systems as large as 40 x 10(6) nodes and over 1 x 10(9) edges. A previous stumbling block encountered by popular community detection methods is the so-called "resolution limit." Being a "local" measure of community structure, our Potts model is free from this resolution-limit effect, and it further remains a local measure on weighted and directed graphs. We also address the mitigation of resolution-limit effects for two other popular Potts models.

Uncovering the properties of energy-weighted conformation space networks with a hydrophobic-hydrophilic model

The conformation spaces generated by short hydrophobic-hydrophilic (HP) lattice chains are mapped to conformation space networks (CSNs). The vertices (nodes) of the network are the conformations and the links are the transitions between them. It has been found that these networks have "small-world" properties without considering the interaction energy of the monomers in the chain, i. e. the hydrophobic or hydrophilic amino acids inside the chain. When the weight based on the interaction energy of the monomers in the chain is added to the CSNs, it is found that the weighted networks show the "scale-free" characteristic. In addition, it reveals that there is a connection between the scale-free property of the weighted CSN and the folding dynamics of the chain by investigating the relationship between the scale-free structure of the weighted CSN and the noted parameter Z score. Moreover, the modular (community) structure of weighted CSNs is also studied. These results are helpful to understand the topological properties of the CSN and the underlying free-energy landscapes.

POINeT: protein interactome with sub-network analysis and hub prioritization

BACKGROUND

Protein-protein interactions (PPIs) are critical to every aspect of biological processes. Expansion of all PPIs from a set of given queries often results in a complex PPI network lacking spatiotemporal consideration. Moreover, the reliability of available PPI resources, which consist of low- and high-throughput data, for network construction remains a significant challenge. Even though a number of software tools are available to facilitate PPI network analysis, an integrated tool is crucial to alleviate the burden on querying across multiple web servers and software tools.

RESULTS

We have constructed an integrated web service, POINeT, to simplify the process of PPI searching, analysis, and visualization. POINeT merges PPI and tissue-specific expression data from multiple resources. The tissue-specific PPIs and the numbers of research papers supporting the PPIs can be filtered with user-adjustable threshold values and are dynamically updated in the viewer. The network constructed in POINeT can be readily analyzed with, for example, the built-in centrality calculation module and an integrated network viewer. Nodes in global networks can also be ranked and filtered using various network analysis formulas, i.e., centralities. To prioritize the sub-network, we developed a ranking filtered method (S3) to uncover potential novel mediators in the midbody network. Several examples are provided to illustrate the functionality of POINeT. The network constructed from four schizophrenia risk markers suggests that EXOC4 might be a novel marker for this disease. Finally, a liver-specific PPI network has been filtered with adult and fetal liver expression profiles.

CONCLUSION

The functionalities provided by POINeT are highly improved compared to previous version of POINT. POINeT enables the identification and ranking of potential novel genes involved in a sub-network. Combining with tissue-specific gene expression profiles, PPIs specific to selected tissues can be revealed. The straightforward interface of POINeT makes PPI search and analysis just a few clicks away. The modular design permits further functional enhancement without hampering the simplicity. POINeT is available at (http://poinet.bioinformatics.tw/).

A Fully Automated Method for Discovering Community Structures in High Dimensional Data

Identifying modules, or natural communities, in large complex networks is fundamental in many fields, including social sciences, biological sciences and engineering. Recently several methods have been developed to automatically identify communities from complex networks by optimizing the modularity function. The advantage of this type of approaches is that the algorithm does not require any parameter to be tuned. However, the modularity-based methods for community discovery assume that the network structure is given explicitly and is correct. In addition, these methods work best if the network is unweighted and/or sparse. In reality, networks are often not directly defined, or may be given as an affinity matrix. In the first case, each node of the network is defined as a point in a high dimensional space and different networks can be obtained with different network construction methods, resulting in different community structures. In the second case, an affinity matrix may define a dense weighted graph, for which modularity-based methods do not perform well. In this work, we propose a very simple algorithm to automatically identify community structures from these two types of data. Our approach utilizes a k-nearest-neighbor network construction method to capture the topology embedded in high dimensional data, and applies a modularity-based algorithm to identify the optimal community structure. A key to our approach is that the network construction is incorporated with the community identification process and is totally parameter-free. Furthermore, our method can suggest appropriate preprocessing/normalization of the data to improve the results of community identification. We tested our methods on several synthetic and real data sets, and evaluated its performance by internal or external accuracy indices. Compared with several existing approaches, our method is not only fully automatic, but also has the best accuracy overall.

Multistep greedy algorithm identifies community structure in real-world and computer-generated networks

We have recently introduced a multistep extension of the greedy algorithm for modularity optimization. The extension is based on the idea that merging l pairs of communities (l>1) at each iteration prevents premature condensation into few large communities. Here, an empirical formula is presented for the choice of the step width l that generates partitions with (close to) optimal modularity for 17 real-world and 1100 computer-generated networks. Furthermore, an in-depth analysis of the communities of two real-world networks (the metabolic network of the bacterium E. coli and the graph of coappearing words in the titles of papers coauthored by Martin Karplus) provides evidence that the partition obtained by the multistep greedy algorithm is superior to the one generated by the original greedy algorithm not only with respect to modularity, but also according to objective criteria. In other words, the multistep extension of the greedy algorithm reduces the danger of getting trapped in local optima of modularity and generates more reasonable partitions.

Comparative definition of community and corresponding identifying algorithm

A comparative definition for community in networks is proposed, and the corresponding detecting algorithm is given. A community is defined as a set of nodes, which satisfies the requirement that each node's degree inside the community should not be smaller than the node's degree toward any other community. In the algorithm, the attractive force of a community to a node is defined as the connections between them. Then employing an attractive-force-based self-organizing process, without any extra parameter, the best communities can be detected. Several artificial and real-world networks, including the Zachary karate club, college football, and large scientific collaboration networks, are analyzed. The algorithm works well in detecting communities, and it also gives a nice description of network division and group formation.

Community detection by signaling on complex networks

Based on a signaling process of complex networks, a method for identification of community structure is proposed. For a network with n nodes, every node is assumed to be a system which can send, receive, and record signals. Each node is taken as the initial signal source to excite the whole network one time. Then the source node is associated with an n -dimensional vector which records the effects of the signaling process. By this process, the topological relationship of nodes on the network could be transferred into a geometrical structure of vectors in n -dimensional Euclidean space. Then the best partition of groups is determined by F statistics and the final community structure is given by the K -means clustering method. This method can detect community structure both in unweighted and weighted networks. It has been applied to ad hoc networks and some real networks such as the Zachary karate club network and football team network. The results indicate that the algorithm based on the signaling process works well.

Quantitative function for community detection

We propose a quantitative function for community partition -- i.e., modularity density or D value. We demonstrate that this quantitative function is superior to the widely used modularity Q and also prove its equivalence with the objective function of the kernel k means. Both theoretical and numerical results show that optimizing the new criterion not only can resolve detailed modules that existing approaches cannot achieve, but also can correctly identify the number of communities.

Identifying network communities with a high resolution

Community structure is an important property of complex networks. The automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a modularity function (Q) . However, the problem of modularity optimization is NP-hard and the existing approaches often suffer from a prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing Q will have a resolution limit; i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm QCUT, which combines spectral graph partitioning and local search to optimize Q . Using both synthetic and real networks, we show that QCUT can find higher modularities and is more scalable than the existing algorithms. Furthermore, using QCUT as an essential component, we propose a recursive algorithm HQCUT to solve the resolution limit problem. We show that HQCUT can successfully detect communities at a much finer scale or with a higher accuracy than the existing algorithms. We also discuss two possible reasons that can cause the resolution limit problem and provide a method to distinguish them. Finally, we apply QCUT and HQCUT to study a protein-protein interaction network and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetected.

Uncovering fuzzy community structure in complex networks

There has been an increasing interest in properties of complex networks, such as small-world property, power-law degree distribution, and network transitivity which seem to be common to many real world networks. In this study, a useful community detection method based on non-negative matrix factorization (NMF) technique is presented. Based on a popular modular function, a proper feature matrix from diffusion kernel and NMF algorithm, the presented method can detect an appropriate number of fuzzy communities in which a node may belong to more than one community. The distinguished characteristic of the method is its capability of quantifying how much a node belongs to a community. The quantification provides an absolute membership degree for each node to each community which can be employed to uncover fuzzy community structure. The computational results of the method on artificial and real networks confirm its ability.

A network partition algorithm for mining gene functional modules of colon cancer from DNA microarray data

Computational analysis is essential for transforming the masses of microarray data into a mechanistic understanding of cancer. Here we present a method for finding gene functional modules of cancer from microarray data and have applied it to colon cancer. First, a colon cancer gene network and a normal colon tissue gene network were constructed using correlations between the genes. Then the modules that tended to have a homogeneous functional composition were identified by splitting up the network. Analysis of both networks revealed that they are scale-free. Comparison of the gene functional modules for colon cancer and normal tissues showed that the modules’ functions changed with their structures.

Characterization of protein-interaction networks in tumors

BACKGROUND

Analyzing differential-gene-expression data in the context of protein-interaction networks (PINs) yields information on the functional cellular status. PINs can be formally represented as graphs, and approximating PINs as undirected graphs allows the network properties to be characterized using well-established graph measures. This paper outlines features of PINs derived from 29 studies on differential gene expression in cancer. For each study the number of differentially regulated genes was determined and used as a basis for PIN construction utilizing the Online Predicted Human Interaction Database.

RESULTS

Graph measures calculated for the largest subgraph of a PIN for a given differential-gene-expression data set comprised properties reflecting the size, distribution, biological relevance, density, modularity, and cycles. The values of a distinct set of graph measures, namely Closeness Centrality, Graph Diameter, Index of Aggregation, Assortative Mixing Coefficient, Connectivity, Sum of the Wiener Number, modified Vertex Distance Number, and Eigenvalues differed clearly between PINs derived on the basis of differential gene expression data sets characterizing malignant tissue and PINs derived on the basis of randomly selected protein lists.

CONCLUSION

Cancer PINs representing differentially regulated genes are larger than those of randomly selected protein lists, indicating functional dependencies among protein lists that can be identified on the basis of transcriptomics experiments. However, the prevalence of hub proteins was not increased in the presence of cancer. Interpretation of such graphs in the context of robustness may yield novel therapies based on synthetic lethality that are more effective than focusing on single-action drugs for cancer treatment.

Complex network analysis of free-energy landscapes

The kinetics of biomolecular isomerization processes, such as protein folding, is governed by a free-energy surface of high dimensionality and complexity. As an alternative to projections into one or two dimensions, the free-energy surface can be mapped into a weighted network where nodes and links are configurations and direct transitions among them, respectively. In this work, the free-energy basins and barriers of the alanine dipeptide are determined quantitatively using an algorithm to partition the network into clusters (i.e., states) according to the equilibrium transitions sampled by molecular dynamics. The network-based approach allows for the analysis of the thermodynamics and kinetics of biomolecule isomerization without reliance on arbitrarily chosen order parameters. Moreover, it is shown on low-dimensional models, which can be treated analytically, as well as for the alanine dipeptide, that the broad-tailed weight distribution observed in their networks originates from free-energy basins with mainly enthalpic character.

Resolution limit in community detection

Detecting community structure is fundamental for uncovering the links between structure and function in complex networks and for practical applications in many disciplines such as biology and sociology. A popular method now widely used relies on the optimization of a quantity called modularity, which is a quality index for a partition of a network into communities. We find that modularity optimization may fail to identify modules smaller than a scale which depends on the total size of the network and on the degree of interconnectedness of the modules, even in cases where modules are unambiguously defined. This finding is confirmed through several examples, both in artificial and in real social, biological, and technological networks, where we show that modularity optimization indeed does not resolve a large number of modules. A check of the modules obtained through modularity optimization is thus necessary, and we provide here key elements for the assessment of the reliability of this community detection method.

Network of epicenters of the Olami-Feder-Christensen model of earthquakes

We study the dynamics of the Olami-Feder-Christensen (OFC) model of earthquakes, focusing on the behavior of sequences of epicenters regarded as a growing complex network. Besides making a detailed and quantitative study of the effects of the borders (the occurrence of epicenters is dominated by a strong border effect which does not scale with system size), we examine the degree distribution and the degree correlation of the graph. We detect sharp differences between the conservative and nonconservative regimes of the model. Removing border effects, the conservative regime exhibits a Poisson-like degree statistics and is uncorrelated, while the nonconservative has a broad power-law-like distribution of degrees (if the smallest events are ignored), which reproduces the observed behavior of real earthquakes. In this regime the graph has also an unusually strong degree correlation among the vertices with higher degree, which is the result of the existence of temporary attractors for the dynamics: as the system evolves, the epicenters concentrate increasingly on fewer sites, exhibiting strong synchronization, but eventually spread again over the lattice after a series of sufficiently large earthquakes. We propose an analytical description of the dynamics of this growing network, considering a Markov process network with hidden variables, which is able to account for the mentioned properties.

Statistical mechanics of community detection

Starting from a general ansatz, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the ad hoc introduced quality function from [J. Reichardt and S. Bornholdt, Phys. Rev. Lett. 93, 218701 (2004)] and the modularity Q as defined by Newman and Girvan [Phys. Rev. E 69, 026113 (2004)] as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further, we show how hierarchies and overlap in the community structure can be detected. Computationally efficient local update rules for optimization procedures to find the ground state are given. We show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure.