Module identification in bipartite and directed networks

Improved community detection in weighted bipartite networks

Real-world complex networks are composed of non-random quantitative interactions. Identifying communities of nodes that tend to interact more with each other than the network as a whole is a key research focus across multiple disciplines, yet many community detection algorithms only use information about the presence or absence of interactions between nodes. Weighted modularity is a potential method for evaluating the quality of community partitions in quantitative networks. In this framework, the optimal community partition of a network can be found by searching for the partition that maximizes modularity. Attempting to find the partition that maximizes modularity is a computationally hard problem requiring the use of algorithms. QuanBiMo is an algorithm that has been proposed to maximize weighted modularity in bipartite networks. This paper introduces two new algorithms, LPAwb+ and DIRTLPAwb+, for maximizing weighted modularity in bipartite networks. LPAwb+ and DIRTLPAwb+ robustly identify partitions with high modularity scores. DIRTLPAwb+ consistently matched or outperformed QuanBiMo, while the speed of LPAwb+ makes it an attractive choice for detecting the modularity of larger networks. Searching for modules using weighted data (rather than binary data) provides a different and potentially insightful method for evaluating network partitions.

Improved community detection in weighted bipartite networks

Real-world complex networks are composed of non-random quantitative interactions. Identifying communities of nodes that tend to interact more with each other than the network as a whole is a key research focus across multiple disciplines, yet many community detection algorithms only use information about the presence or absence of interactions between nodes. Weighted modularity is a potential method for evaluating the quality of community partitions in quantitative networks. In this framework, the optimal community partition of a network can be found by searching for the partition that maximizes modularity. Attempting to find the partition that maximizes modularity is a computationally hard problem requiring the use of algorithms. QuanBiMo is an algorithm that has been proposed to maximize weighted modularity in bipartite networks. This paper introduces two new algorithms, LPAwb+ and DIRTLPAwb+, for maximizing weighted modularity in bipartite networks. LPAwb+ and DIRTLPAwb+ robustly identify partitions with high modularity scores. DIRTLPAwb+ consistently matched or outperformed QuanBiMo, while the speed of LPAwb+ makes it an attractive choice for detecting the modularity of larger networks. Searching for modules using weighted data (rather than binary data) provides a different and potentially insightful method for evaluating network partitions.

Emerging landscape of oncogenic signatures across human cancers

Cancer therapy is challenged by the diversity of molecular implementations of oncogenic processes and by the resulting variation in therapeutic responses. Projects such as The Cancer Genome Atlas (TCGA) provide molecular tumor maps in unprecedented detail. The interpretation of these maps remains a major challenge. Here we distilled thousands of genetic and epigenetic features altered in cancers to ~500 selected functional events (SFEs). Using this simplified description, we derived a hierarchical classification of 3,299 TCGA tumors from 12 cancer types. The top classes are dominated by either mutations (M class) or copy number changes (C class). This distinction is clearest at the extremes of genomic instability, indicating the presence of different oncogenic processes. The full hierarchy shows functional event patterns characteristic of multiple cross-tissue groups of tumors, termed oncogenic signature classes. Targetable functional events in a tumor class are suggestive of class-specific combination therapy. These results may assist in the definition of clinical trials to match actionable oncogenic signatures with personalized therapies.

Trophic groups and modules: two levels of group detection in food webs

Within food webs, species can be partitioned into groups according to various criteria. Two notions have received particular attention: trophic groups (TGs), which have been used for decades in the ecological literature, and more recently, modules. The relationship between these two group concepts remains unknown in empirical food webs. While recent developments in network theory have led to efficient methods for detecting modules in food webs, the determination of TGs (groups of species that are functionally similar) is largely based on subjective expert knowledge. We develop a novel algorithm for TG detection. We apply this method to empirical food webs and show that aggregation into TGs allows for the simplification of food webs while preserving their information content. Furthermore, we reveal a two-level hierarchical structure where modules partition food webs into large bottom-top trophic pathways, whereas TGs further partition these pathways into groups of species with similar trophic connections. This provides new perspectives for the study of dynamical and functional consequences of food-web structure, bridging topological and dynamical analysis. TGs have a clear ecological meaning and are found to provide a trade-off between network complexity and information loss.

Bank-firm credit network in Japan: an analysis of a bipartite network

We investigate the networked nature of the Japanese credit market. Our investigation is performed with tools of network science. In our investigation we perform community detection with an algorithm which is identifying communities composed of both banks and firms. We show that the communities obtained by directly working on the bipartite network carry information about the networked nature of the Japanese credit market. Our analysis is performed for each calendar year during the time period from 1980 to 2011. To investigate the time evolution of the networked structure of the credit market we introduce a new statistical method to track the time evolution of detected communities. We then characterize the time evolution of communities by detecting for each time evolving set of communities the over-expression of attributes of firms and banks. Specifically, we consider as attributes the economic sector and the geographical location of firms and the type of banks. In our 32-year-long analysis we detect a persistence of the over-expression of attributes of communities of banks and firms together with a slow dynamic of changes from some specific attributes to new ones. Our empirical observations show that the credit market in Japan is a networked market where the type of banks, geographical location of firms and banks, and economic sector of the firm play a role in shaping the credit relationships between banks and firms.

A modularity-based method reveals mixed modules from chemical-gene heterogeneous network

For a multicomponent therapy, molecular network is essential to uncover its specific mode of action from a holistic perspective. The molecular system of a Traditional Chinese Medicine (TCM) formula can be represented by a 2-class heterogeneous network (2-HN), which typically includes chemical similarities, chemical-target interactions and gene interactions. An important premise of uncovering the molecular mechanism is to identify mixed modules from complex chemical-gene heterogeneous network of a TCM formula. We thus proposed a novel method (MixMod) based on mixed modularity to detect accurate mixed modules from 2-HNs. At first, we compared MixMod with Clauset-Newman-Moore algorithm (CNM), Markov Cluster algorithm (MCL), Infomap and Louvain on benchmark 2-HNs with known module structure. Results showed that MixMod was superior to other methods when 2-HNs had promiscuous module structure. Then these methods were tested on a real drug-target network, in which 88 disease clusters were regarded as real modules. MixMod could identify the most accurate mixed modules from the drug-target 2-HN (normalized mutual information 0.62 and classification accuracy 0.4524). In the end, MixMod was applied to the 2-HN of Buchang naoxintong capsule (BNC) and detected 49 mixed modules. By using enrichment analysis, we investigated five mixed modules that contained primary constituents of BNC intestinal absorption liquid. As a matter of fact, the findings of in vitro experiments using BNC intestinal absorption liquid were found to highly accord with previous analysis. Therefore, MixMod is an effective method to detect accurate mixed modules from chemical-gene heterogeneous networks and further uncover the molecular mechanism of multicomponent therapies, especially TCM formulae.

Mining the modular structure of protein interaction networks

BACKGROUND

Cluster-based descriptions of biological networks have received much attention in recent years fostered by accumulated evidence of the existence of meaningful correlations between topological network clusters and biological functional modules. Several well-performing clustering algorithms exist to infer topological network partitions. However, due to respective technical idiosyncrasies they might produce dissimilar modular decompositions of a given network. In this contribution, we aimed to analyze how alternative modular descriptions could condition the outcome of follow-up network biology analysis.

METHODOLOGY

We considered a human protein interaction network and two paradigmatic cluster recognition algorithms, namely: the Clauset-Newman-Moore and the infomap procedures. We analyzed to what extent both methodologies yielded different results in terms of granularity and biological congruency. In addition, taking into account Guimera's cartographic role characterization of network nodes, we explored how the adoption of a given clustering methodology impinged on the ability to highlight relevant network meso-scale connectivity patterns.

RESULTS

As a case study we considered a set of aging related proteins and showed that only the high-resolution modular description provided by infomap, could unveil statistically significant associations between them and inter/intra modular cartographic features. Besides reporting novel biological insights that could be gained from the discovered associations, our contribution warns against possible technical concerns that might affect the tools used to mine for interaction patterns in network biology studies. In particular our results suggested that sub-optimal partitions from the strict point of view of their modularity levels might still be worth being analyzed when meso-scale features were to be explored in connection with external source of biological knowledge.

Network community structure detection for directional neural networks inferred from multichannel multisubject EEG data

In many neuroscience applications, one is interested in identifying the functional brain modules from multichannel, multiple subject neuroimaging data. However, most of the existing network community structure detection algorithms are limited to single undirected networks and cannot reveal the common community structure for a collection of directed networks. In this paper, we propose a community detection algorithm for weighted asymmetric (directed) networks representing the effective connectivity in the brain. Moreover, the issue of finding a common community structure across subjects is addressed by maximizing the total modularity of the group. Finally, the proposed community detection algorithm is applied to multichannel multisubject electroencephalogram data.

Potential parasite transmission in multi-host networks based on parasite sharing

Epidemiological networks are commonly used to explore dynamics of parasite transmission among individuals in a population of a given host species. However, many parasites infect multiple host species, and thus multi-host networks may offer a better framework for investigating parasite dynamics. We investigated the factors that influence parasite sharing--and thus potential transmission pathways--among rodent hosts in Southeast Asia. We focused on differences between networks of a single host species and networks that involve multiple host species. In host-parasite networks, modularity (the extent to which the network is divided into subgroups of rodents that interact with similar parasites) was higher in the multi-species than in the single-species networks. This suggests that phylogeny affects patterns of parasite sharing, which was confirmed in analyses showing that it predicted affiliation of individuals to modules. We then constructed "potential transmission networks" based on the host-parasite networks, in which edges depict the similarity between a pair of individuals in the parasites they share. The centrality of individuals in these networks differed between multi- and single-species networks, with species identity and individual characteristics influencing their position in the networks. Simulations further revealed that parasite dynamics differed between multi- and single-species networks. We conclude that multi-host networks based on parasite sharing can provide new insights into the potential for transmission among hosts in an ecological community. In addition, the factors that determine the nature of parasite sharing (i.e. structure of the host-parasite network) may impact transmission patterns.

Identifying Driver Nodes in the Human Signaling Network Using Structural Controllability Analysis

Cell signaling governs the basic cellular activities and coordinates the actions in cell. Abnormal regulations in cell signaling processing are responsible for many human diseases, such as diabetes and cancers. With the accumulation of massive data related to human cell signaling, it is feasible to obtain a human signaling network. Some studies have shown that interesting biological phenomenon and drug-targets could be discovered by applying structural controllability analysis to biological networks. In this work, we apply structural controllability to a human signaling network and detect driver nodes, providing a systematic analysis of the role of different proteins in controlling the human signaling network. We find that the proteins in the upstream of the signaling information flow and the low in-degree proteins play a crucial role in controlling the human signaling network. Interestingly, inputting different control signals on the regulators of the cancer-associated genes could cost less than controlling the cancer-associated genes directly in order to control the whole human signaling network in the sense that less drive nodes are needed. This research provides a fresh perspective for controlling the human cell signaling system.

Concomitant predation on parasites is highly variable but constrains the ways in which parasites contribute to food web structure

Previous analyses of empirical food webs (the networks of who eats whom in a community) have revealed that parasites exert a strong influence over observed food web structure and alter many network properties such as connectance and degree distributions. It remains unclear, however, whether these community‐level effects are fully explained by differences in the ways that parasites and free‐living species interact within a food web.

To rigorously quantify the interrelationship between food web structure, the types of species in a web and the distinct types of feeding links between them, we introduce a shared methodology to quantify the structural roles of both species and feeding links. Roles are quantified based on the frequencies with which a species (or link) appears in different food web motifs – the building blocks of networks.

We hypothesized that different types of species (e.g. top predators, basal resources, parasites) and different types of links between species (e.g. classic predation, parasitism, concomitant predation on parasites along with their hosts) will show characteristic differences in their food web roles.

We found that parasites do indeed have unique structural roles in food webs. Moreover, we demonstrate that different types of feeding links (e.g. parasitism, predation or concomitant predation) are distributed differently in a food web context. More than any other interaction type, concomitant predation appears to constrain the roles of parasites. In contrast, concomitant predation links themselves have more variable roles than any other type of interaction.

Together, our results provide a novel perspective on how both species and feeding link composition shape the structure of an ecological community and vice versa.

Bidirectional selection between two classes in complex social networks

The bidirectional selection between two classes widely emerges in various social lives, such as commercial trading and mate choosing. Until now, the discussions on bidirectional selection in structured human society are quite limited. We demonstrated theoretically that the rate of successfully matching is affected greatly by individuals' neighborhoods in social networks, regardless of the type of networks. Furthermore, it is found that the high average degree of networks contributes to increasing rates of successful matches. The matching performance in different types of networks has been quantitatively investigated, revealing that the small-world networks reinforces the matching rate more than scale-free networks at given average degree. In addition, our analysis is consistent with the modeling result, which provides the theoretical understanding of underlying mechanisms of matching in complex networks.

Cluster analysis of weighted bipartite networks: a new copula-based approach

In this work we are interested in identifying clusters of “positional equivalent” actors, i.e. actors who play a similar role in a system. In particular, we analyze weighted bipartite networks that describes the relationships between actors on one side and features or traits on the other, together with the intensity level to which actors show their features. We develop a methodological approach that takes into account the underlying multivariate dependence among groups of actors. The idea is that positions in a network could be defined on the basis of the similar intensity levels that the actors exhibit in expressing some features, instead of just considering relationships that actors hold with each others. Moreover, we propose a new clustering procedure that exploits the potentiality of copula functions, a mathematical instrument for the modelization of the stochastic dependence structure. Our clustering algorithm can be applied both to binary and real-valued matrices. We validate it with simulations and applications to real-world data.

Efficiently inferring community structure in bipartite networks

Bipartite networks are a common type of network data in which there are two types of vertices, and only vertices of different types can be connected. While bipartite networks exhibit community structure like their unipartite counterparts, existing approaches to bipartite community detection have drawbacks, including implicit parameter choices, loss of information through one-mode projections, and lack of interpretability. Here we solve the community detection problem for bipartite networks by formulating a bipartite stochastic block model, which explicitly includes vertex type information and may be trivially extended to k-partite networks. This bipartite stochastic block model yields a projection-free and statistically principled method for community detection that makes clear assumptions and parameter choices and yields interpretable results. We demonstrate this model's ability to efficiently and accurately find community structure in synthetic bipartite networks with known structure and in real-world bipartite networks with unknown structure, and we characterize its performance in practical contexts.

Exploring community structure in biological networks with random graphs

Background

Community structure is ubiquitous in biological networks. There has been an increased interest in unraveling the community structure of biological systems as it may provide important insights into a system’s functional components and the impact of local structures on dynamics at a global scale. Choosing an appropriate community detection algorithm to identify the community structure in an empirical network can be difficult, however, as the many algorithms available are based on a variety of cost functions and are difficult to validate. Even when community structure is identified in an empirical system, disentangling the effect of community structure from other network properties such as clustering coefficient and assortativity can be a challenge.

Results

Here, we develop a generative model to produce undirected, simple, connected graphs with a specified degrees and pattern of communities, while maintaining a graph structure that is as random as possible. Additionally, we demonstrate two important applications of our model: (a) to generate networks that can be used to benchmark existing and new algorithms for detecting communities in biological networks; and (b) to generate null models to serve as random controls when investigating the impact of complex network features beyond the byproduct of degree and modularity in empirical biological networks.

Conclusion

Our model allows for the systematic study of the presence of community structure and its impact on network function and dynamics. This process is a crucial step in unraveling the functional consequences of the structural properties of biological systems and uncovering the mechanisms that drive these systems.

Climatic seasonality may affect ecological network structure: food webs and mutualistic networks

Ecological networks exhibit non-random structural patterns, such as modularity and nestedness, which determine ecosystem stability with species diversity and connectance. Such structure-stability relationships are well known. However, another important perspective is less well understood: the relationship between the environment and structure. Inspired by theoretical studies that suggest that network structure can change due to environmental variability, we collected data on a number of empirical food webs and mutualistic networks and evaluated the effect of climatic seasonality on ecological network structure. As expected, we found that climatic seasonality affects ecological network structure. In particular, an increase in modularity due to climatic seasonality was observed in food webs; however, it is debatable whether this occurs in mutualistic networks. Interestingly, the type of climatic seasonality that affects network structure differs with ecosystem type. Rainfall and temperature seasonality influence freshwater food webs and mutualistic networks, respectively; food webs are smaller, and more modular, with increasing rainfall seasonality. Mutualistic networks exhibit a higher diversity (particularly of animals) with increasing temperature seasonality. These results confirm the theoretical prediction that the stability increases with greater perturbation. Although these results are still debatable because of several limitations in the data analysis, they may enhance our understanding of environment-structure relationships.

Community structures in bipartite networks: a dual-projection approach

Identifying communities or clusters in networked systems has received much attention across the physical and social sciences. Most of this work focuses on single layer or one-mode networks, including social networks between people or hyperlinks between websites. Multilayer or multi-mode networks, such as affiliation networks linking people to organizations, receive much less attention in this literature. Common strategies for discovering the community structure of multi-mode networks identify the communities of each mode simultaneously. Here I show that this combined approach is ineffective at discovering community structures when there are an unequal number of communities between the modes of a multi-mode network. I propose a dual-projection alternative for detecting communities in multi-mode networks that overcomes this shortcoming. The evaluation of synthetic networks with known community structures reveals that the dual-projection approach outperforms the combined approach when there are a different number of communities in the various modes. At the same time, results show that the dual-projection approach is as effective as the combined strategy when the number of communities is the same between the modes.

A collaborative recommend algorithm based on bipartite community

The recommendation algorithm based on bipartite network is superior to traditional methods on accuracy and diversity, which proves that considering the network topology of recommendation systems could help us to improve recommendation results. However, existing algorithms mainly focus on the overall topology structure and those local characteristics could also play an important role in collaborative recommend processing. Therefore, on account of data characteristics and application requirements of collaborative recommend systems, we proposed a link community partitioning algorithm based on the label propagation and a collaborative recommendation algorithm based on the bipartite community. Then we designed numerical experiments to verify the algorithm validity under benchmark and real database.

A model of two-way selection system for human behavior

Two-way selection is a common phenomenon in nature and society. It appears in the processes like choosing a mate between men and women, making contracts between job hunters and recruiters, and trading between buyers and sellers. In this paper, we propose a model of two-way selection system, and present its analytical solution for the expectation of successful matching total and the regular pattern that the matching rate trends toward an inverse proportion to either the ratio between the two sides or the ratio of the state total to the smaller group's people number. The proposed model is verified by empirical data of the matchmaking fairs. Results indicate that the model well predicts this typical real-world two-way selection behavior to the bounded error extent, thus it is helpful for understanding the dynamics mechanism of the real-world two-way selection system.

Evolution of pollination niches and floral divergence in the generalist plant Erysimum mediohispanicum

BACKGROUND AND AIMS

How generalist plants diverge in response to pollinator selection without becoming specialized is still unknown. This study explores this question, focusing on the evolution of the pollination system in the pollination generalist Erysimum mediohispanicum (Brassicaceae).

METHODS

Pollinator assemblages were surveyed from 2001 to 2010 in 48 geo-referenced populations covering the entire geographic distribution of E. mediohispanicum. Bipartite modularity, a complex network tool, was used to find the pollination niche of each population. Evolution of the pollination niches and the correlated evolution of floral traits and pollination niches were explored using within-species comparative analyses.

KEY RESULTS

Despite being generalists, the E. mediohispanicum populations studied can be classified into five pollination niches. The boundaries between niches were not sharp, the niches differing among them in the relative frequencies of the floral visitor functional groups. The absence of spatial autocorrelation and phylogenetic signal indicates that the niches were distributed in a phylogeographic mosaic. The ancestral E. mediohispanicum populations presumably belonged to the niche defined by a high number of beetle and ant visits. A correlated evolution was found between pollination niches and some floral traits, suggesting the existence of generalist pollination ecotypes.

CONCLUSIONS

It is conjectured that the geographic variation in pollination niches has contributed to the observed floral divergence in E. mediohispanicum. The process mediating this floral divergence presumably has been adaptive wandering, but the adaptation to the local pollinator faunas has been not universal. The outcome is a landscape where a few populations locally adapted to their pollination environment (generalist pollination ecotypes) coexist with many populations where this local adaptation has failed and where the plant phenotype is not primarily shaped by pollinators.

Community analysis in directed networks: in-, out-, and pseudocommunities

When analyzing important classes of complex interconnected systems, link directionality can hardly be neglected if a precise and effective picture of the structure and function of the system is needed. If community analysis is performed, the notion of "community" itself is called into question, since the property of having a comparatively looser external connectivity could refer to the inbound or outbound links only or to both categories. In this paper, we introduce the notions of in-, out-, and in-/out-community in order to correctly classify the directedness of the interaction of a subnetwork with the rest of the system. Furthermore, we extend the scope of community analysis by introducing the notions of in-, out-, and in-/out-pseudocommunity. They are subnetworks having strong internal connectivity but also important interactions with the rest of the system, the latter taking place by means of a minority of its nodes only. The various types of (pseudo-)communities are qualified and distinguished by a suitable set of indicators and, on a given network, they can be discovered by using a "local" searching algorithm. The application to a broad set of benchmark networks and real-world examples proves that the proposed approach is able to effectively disclose the different types of structures above defined and to usefully classify the directionality of their interactions with the rest of the system.

MCF: a tool to find multi-scale community profiles in biological networks

Recent developments of complex graph clustering methods have implicated the practical applications with biological networks in different settings. Multi-scale Community Finder (MCF) is a tool to profile network communities (i.e., clusters of nodes) with the control of community sizes. The controlling parameter is referred to as the scale of the network community profile. MCF is able to find communities in all major types of networks including directed, signed, bipartite, and multi-slice networks. The fast computation promotes the practicability of the tool for large-scaled analysis (e.g., protein-protein interaction and gene co-expression networks). MCF is distributed as an open-source C++ package for academic use with both command line and user interface options, and can be downloaded at http://bsdxd.cpsc.ucalgary.ca/MCF. Detailed user manual and sample data sets are also available at the project website.

The role of complementary bipartite visual analytical representations in the analysis of SNPs: a case study in ancestral informative markers

Objective

Several studies have shown how sets of single-nucleotide polymorphisms (SNPs) can help to classify subjects on the basis of their continental origins, with applications to case–control studies and population genetics. However, most of these studies use dimensionality-reduction methods, such as principal component analysis, or clustering methods that result in unipartite (either subjects or SNPs) representations of the data. Such analyses conceal important bipartite relationships, such as how subject and SNP clusters relate to each other, and the genotypes that determine their cluster memberships.

Methods

To overcome the limitations of current methods of analyzing SNP data, the authors used three bipartite analytical representations (bipartite network, heat map with dendrograms, and Circos ideogram) that enable the simultaneous visualization and analysis of subjects, SNPs, and subject attributes.

Results

The results demonstrate (1) novel insights into SNP data that are difficult to derive from purely unipartite views of the data, (2) the strengths and limitations of each method, revealing the role that each play in revealing novel insights, and (3) implications for how the methods can be used for the analysis of SNPs in genomic studies associated with disease.

Conclusion

The results suggest that bipartite representations can reveal new patterns in SNP data compared with existing unipartite representations. However, the novel insights require multiple representations to discover, verify, and comprehend the complex relationships. The results therefore motivate the need for a complementary visual analytical framework that guides the use of multiple bipartite representations to analyze complex relationships in SNP data.

Assessing the robustness of networks of spatial genetic variation

Habitat transformation is one of the leading drivers of biodiversity loss. The ecological effects of this transformation have mainly been addressed at the demographic level, for example, finding extinction thresholds. However, interpopulation genetic variability and the subsequent potential for adaptation can be eroded before effects are noticed on species abundances. To what degree this is the case has been difficult to evaluate, partly because of the lack of both spatially extended genetic data and an appropriate framework to map and analyse such data. Here, we extend recent work on the analysis of networks of spatial genetic variation to address the robustness of these networks in the face of perturbations. We illustrate the potential of this framework using the case study of an amphibian metapopulation. Our results show that while the disappearance of some spatial sites barely changes the modular structure of the genetic network, other sites have a much stronger effect. Interestingly, these consequences can not be anticipated using topological, static measures. Mapping these networks of spatial genetic variation will allow identifying significant evolutionary units and how they vanish, merge and reorganise following perturbations.

Increasing functional modularity with residence time in the co-distribution of native and introduced vascular plants

Species gain membership of regional assemblages by passing through multiple ecological and environmental filters. To capture the potential trajectory of structural changes in regional meta-communities driven by biological invasions, one can categorize species pools into assemblages of different residence times. Older assemblages, having passed through more environmental filters, should become more functionally ordered and structured. Here we calculate the level of compartmentalization (modularity) for three different-aged assemblages (neophytes, introduced after 1500 AD; archaeophytes, introduced before 1500 AD, and natives), including 2,054 species of vascular plants in 302 reserves in central Europe. Older assemblages are more compartmentalized than younger ones, with species composition, phylogenetic structure and habitat characteristics of the modules becoming increasingly distinctive. This sheds light on two mechanisms of how alien species are functionally incorporated into regional species pools: the settling-down hypothesis of diminishing stochasticity with residence time, and the niche-mosaic hypothesis of inlaid neutral modules in regional meta-communities.

Phage-bacteria infection networks

Phage and their bacterial hosts are the most abundant and genetically diverse group of organisms on the planet. Given their dominance, it is no wonder that many recent studies have found that phage-bacteria interactions strongly influence global biogeochemical cycles, incidence of human diseases, productivity of industrial microbial commodities, and patterns of microbial genome diversity. Unfortunately, given the extreme diversity and complexity of microbial communities, traditional analyses fail to characterize interaction patterns and underlying processes. Here, we review emerging systems approaches that combine empirical data with rigorous theoretical analysis to study phage-bacterial interactions as networks rather than as coupled interactions in isolation.

Alignment and integration of complex networks by hypergraph-based spectral clustering

Complex networks possess a rich, multiscale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one type of interaction, or to go beyond simple pairwise interactions, but currently there is a lack of theoretical and computational methods to address these problems. Here we introduce a framework for clustering and community detection in such systems using hypergraph representations. Our main result is a generalization of the Perron-Frobenius theorem from which we derive spectral clustering algorithms for directed and undirected hypergraphs. We illustrate our approach with applications for local and global alignment of protein-protein interaction networks between multiple species, for tripartite community detection in folksonomies, and for detecting clusters of overlapping regulatory pathways in directed networks.

Identifying Overlying Group of People through Clustering

Folksonomies like Delicious and LastFm are modeled as multilateral (user-resource-tag) hypergraphs for studying their network properties. Detecting communities of similar nodes from such networks is a challenging problem. Most existing algorithms for community detection in folksonomies assign unique communities to nodes, whereas in reality, users have multiple relevant interests and same resource is often tagged with semantically different tags. Few attempts to perceive overlapping communities work on forecasts of hypergraph, which results in momentous loss of information contained in original tripartite structure. Propose first algorithm to detect overlapping communities in folksonomies using complete hypergraph structure. The authors’ algorithm converts a hypergraph into its parallel line graph, using measures of hyperedge similarity, whereby any community detection algorithm on unipartite graphs can be used to produce intersecting communities in folksonomy. Through extensive experiments on synthetic as well as real folksonomy data, demonstrate that proposed algorithm can detect better community structures as compared to existing state-of-the-art algorithms for folksonomies.

Artefacts in statistical analyses of network motifs: general framework and application to metabolic networks

Few-node subgraphs are the smallest collective units in a network that can be investigated. They are beyond the scale of individual nodes but more local than, for example, communities. When statistically over- or under-represented, they are called network motifs. Network motifs have been interpreted as building blocks that shape the dynamic behaviour of networks. It is this promise of potentially explaining emergent properties of complex systems with relatively simple structures that led to an interest in network motifs in an ever-growing number of studies and across disciplines. Here, we discuss artefacts in the analysis of network motifs arising from discrepancies between the network under investigation and the pool of random graphs serving as a null model. Our aim was to provide a clear and accessible catalogue of such incongruities and their effect on the motif signature. As a case study, we explore the metabolic network of Escherichia coli and show that only by excluding ever more artefacts from the motif signature a strong and plausible correlation with the essentiality profile of metabolic reactions emerges.

Modularity in protein complex and drug interactions reveals new polypharmacological properties

Recent studies have highlighted the importance of interconnectivity in a large range of molecular and human disease-related systems. Network medicine has emerged as a new paradigm to deal with complex diseases. Connections between protein complexes and key diseases have been suggested for decades. However, it was not until recently that protein complexes were identified and classified in sufficient amounts to carry out a large-scale analysis of the human protein complex system. We here present the first systematic and comprehensive set of relationships between protein complexes and associated drugs and analyzed their topological features. The network structure is characterized by a high modularity, both in the bipartite graph and in its projections, indicating that its topology is highly distinct from a random network and that it contains a rich and heterogeneous internal modular structure. To unravel the relationships between modules of protein complexes, drugs and diseases, we investigated in depth the origins of this modular structure in examples of particular diseases. This analysis unveils new associations between diseases and protein complexes and highlights the potential role of polypharmacological drugs, which target multiple cellular functions to combat complex diseases driven by gain-of-function mutations.

Justice blocks and predictability of U.S. Supreme Court votes

Successful attempts to predict judges' votes shed light into how legal decisions are made and, ultimately, into the behavior and evolution of the judiciary. Here, we investigate to what extent it is possible to make predictions of a justice's vote based on the other justices' votes in the same case. For our predictions, we use models and methods that have been developed to uncover hidden associations between actors in complex social networks. We show that these methods are more accurate at predicting justice's votes than forecasts made by legal experts and by algorithms that take into consideration the content of the cases. We argue that, within our framework, high predictability is a quantitative proxy for stable justice (and case) blocks, which probably reflect stable a priori attitudes toward the law. We find that U.S. Supreme Court justice votes are more predictable than one would expect from an ideal court composed of perfectly independent justices. Deviations from ideal behavior are most apparent in divided 5–4 decisions, where justice blocks seem to be most stable. Moreover, we find evidence that justice predictability decreased during the 50-year period spanning from the Warren Court to the Rehnquist Court, and that aggregate court predictability has been significantly lower during Democratic presidencies. More broadly, our results show that it is possible to use methods developed for the analysis of complex social networks to quantitatively investigate historical questions related to political decision-making.

Finding and testing network communities by lumped Markov chains

Identifying communities (or clusters), namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov chain model of a random walker, a quality measure called “persistence probability” is associated to a cluster, which is then defined as an “-community” if such a probability is not smaller than . Consistently, a partition composed of -communities is an “-partition.” These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired -level allows one to immediately select the -partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the quality of each single community. Given its ability in individually assessing each single cluster, this approach can also disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure.

Comment on "Evolutionary method for finding communities in bipartite networks"

In a recent paper, Zhan, Zhang, Guan, and Zhou [Phys. Rev. E 83, 066120 (2011)] presented a modified adaptive genetic algorithm (MAGA) tailored to the discovery of maximum modularity partitions of the node set into communities in unipartite, bipartite, and directed networks. The authors claim that "detection of communities in unipartite networks or in directed networks can be transformed into the same task in bipartite networks." Actually, some tests show that it is not the case for the proposed transformations, and why. Experimental results of MAGA for modularity maximization of untransformed unipartite or bipartite networks are also discussed.

How cytokines co-occur across asthma patients: from bipartite network analysis to a molecular-based classification

Asthmatic patients are currently classified as either severe or non-severe based primarily on their response to glucocorticoids. However, because this classification is based on a post-hoc assessment of treatment response, it does not inform the rational staging of disease or therapy. Recent studies in other diseases suggest that a classification which includes molecular information could lead to more accurate diagnoses and prediction of treatment response. We therefore measured cytokine values in bronchoalveolar lavage (BAL) samples of the lower respiratory tract obtained from 83 asthma patients, and used bipartite network visualizations with associated quantitative measures to conduct an exploratory analysis of the co-occurrence of cytokines across patients. The analysis helped to identify three clusters of patients which had a complex but understandable interaction with three clusters of cytokines, leading to insights for a state-based classification of asthma patients. Furthermore, while the patient clusters were significantly different based on key pulmonary functions, they appeared to have no significant relationship to the current classification of asthma patients. These results suggest the need to define a molecular-based classification of asthma patients, which could improve the diagnosis and treatment of this disease.

Evolutionary method for finding communities in bipartite networks

An important step in unveiling the relation between network structure and dynamics defined on networks is to detect communities, and numerous methods have been developed separately to identify community structure in different classes of networks, such as unipartite networks, bipartite networks, and directed networks. Here, we show that the finding of communities in such networks can be unified in a general framework-detection of community structure in bipartite networks. Moreover, we propose an evolutionary method for efficiently identifying communities in bipartite networks. To this end, we show that both unipartite and directed networks can be represented as bipartite networks, and their modularity is completely consistent with that for bipartite networks, the detection of modular structure on which can be reformulated as modularity maximization. To optimize the bipartite modularity, we develop a modified adaptive genetic algorithm (MAGA), which is shown to be especially efficient for community structure detection. The high efficiency of the MAGA is based on the following three improvements we make. First, we introduce a different measure for the informativeness of a locus instead of the standard deviation, which can exactly determine which loci mutate. This measure is the bias between the distribution of a locus over the current population and the uniform distribution of the locus, i.e., the Kullback-Leibler divergence between them. Second, we develop a reassignment technique for differentiating the informative state a locus has attained from the random state in the initial phase. Third, we present a modified mutation rule which by incorporating related operations can guarantee the convergence of the MAGA to the global optimum and can speed up the convergence process. Experimental results show that the MAGA outperforms existing methods in terms of modularity for both bipartite and unipartite networks.

Uncovering space-independent communities in spatial networks

Many complex systems are organized in the form of a network embedded in space. Important examples include the physical Internet infrastructure, road networks, flight connections, brain functional networks, and social networks. The effect of space on network topology has recently come under the spotlight because of the emergence of pervasive technologies based on geolocalization, which constantly fill databases with people's movements and thus reveal their trajectories and spatial behavior. Extracting patterns and regularities from the resulting massive amount of human mobility data requires the development of appropriate tools for uncovering information in spatially embedded networks. In contrast with most works that tend to apply standard network metrics to any type of network, we argue in this paper for a careful treatment of the constraints imposed by space on network topology. In particular, we focus on the problem of community detection and propose a modularity function adapted to spatial networks. We show that it is possible to factor out the effect of space in order to reveal more clearly hidden structural similarities between the nodes. Methods are tested on a large mobile phone network and computer-generated benchmarks where the effect of space has been incorporated.

Community detection in graphs using singular value decomposition

A spectral algorithm for community detection is presented. The algorithm consists of three stages: (1) matrix factorization of two matrix forms, square signless Laplacian for unipartite graphs and rectangular adjacency matrix for bipartite graphs, using singular value decompostion (SVD); (2) dimensionality reduction using an optimal linear approximation; and (3) clustering vertices using dot products in reduced dimensional space. The algorithm reveals communities in graphs without placing any restriction on the input network type or the output community type. It is applicable on unipartite or bipartite unweighted or weighted networks. It places no requirement on strict community membership and automatically reveals the number of clusters, their respective sizes and overlaps, and hierarchical modular organization. By representing vertices as vectors in real space, expressed as linear combinations of the orthogonal bases described by SVD, orthogonality becomes the metric for classifying vertices into communities. Results on several test and real world networks are presented, including cases where a mix of disjointed, overlapping, or hierarchical communities are known to exist in the network.