Link Community Detection Using Generative Model and Nonnegative Matrix Factorization

Discovery of communities in complex networks is a fundamental data analysis problem with applications in various domains. While most of the existing approaches have focused on discovering communities of nodes, recent studies have shown the advantages and uses of link community discovery in networks. Generative models provide a promising class of techniques for the identification of modular structures in networks, but most generative models mainly focus on the detection of node communities rather than link communities. In this work, we propose a generative model, which is based on the importance of each node when forming links in each community, to describe the structure of link communities. We proceed to fit the model parameters by taking it as an optimization problem, and solve it using nonnegative matrix factorization. Thereafter, in order to automatically determine the number of communities, we extend the above method by introducing a strategy of iterative bipartition. This extended method not only finds the number of communities all by itself, but also obtains high efficiency, and thus it is more suitable to deal with large and unexplored real networks. We test this approach on both synthetic benchmarks and real-world networks including an application on a large biological network, and compare it with two highly related methods. Results demonstrate the superior performance of our approach over competing methods for the detection of link communities.     

Discovering Link Communities in Complex Networks by an Integer Programming Model and a Genetic Algorithm

Identification of communities in complex networks is an important topic and issue in many fields such as sociology, biology, and computer science. Communities are often defined as groups of related nodes or links that correspond to functional subunits in the corresponding complex systems. While most conventional approaches have focused on discovering communities of nodes, some recent studies start partitioning links to find overlapping communities straightforwardly. In this paper, we propose a new quantity function for link community identification in complex networks. Based on this quantity function we formulate the link community partition problem into an integer programming model which allows us to partition a complex network into overlapping communities. We further propose a genetic algorithm for link community detection which can partition a network into overlapping communities without knowing the number of communities. We test our model and algorithm on both artificial networks and real-world networks. The results demonstrate that the model and algorithm are efficient in detecting overlapping community structure in complex networks.     

Network frailty and the geometry of herd immunity

The spread of infectious disease through communities depends fundamentally on the underlying patterns of contacts between individuals. Generally, the more contacts one individual has, the more vulnerable they are to infection during an epidemic. Thus, outbreaks disproportionately impact the most highly connected demographics. Epidemics can then lead, through immunization or removal of individuals, to sparser networks that are more resistant to future transmission of a given disease. Using several classes of contact networks-Poisson, scale-free and small-world-we characterize the structural evolution of a network due to an epidemic in terms of frailty (the degree to which highly connected individuals are more vulnerable to infection) and interference (the extent to which the epidemic cuts off connectivity among the susceptible population that remains following an epidemic). The evolution of the susceptible network over the course of an epidemic differs among the classes of networks; frailty, relative to interference, accounts for an increasing component of network evolution on networks with greater variance in contacts. The result is that immunization due to prior epidemics can provide greater community protection than random vaccination on networks with heterogeneous contact patterns, while the reverse is true for highly structured populations.     

Characterizing the Community Structure of Complex Networks

Background

Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has been so far devoted to the investigation of communities in real networks.

Methodology/Principal Findings

We present a systematic empirical analysis of the statistical properties of communities in large information, communication, technological, biological, and social networks. We find that the mesoscopic organization of networks of the same category is remarkably similar. This is reflected in several characteristics of community structure, which can be used as “fingerprints” of specific network categories. While community size distributions are always broad, certain categories of networks consist mainly of tree-like communities, while others have denser modules. Average path lengths within communities initially grow logarithmically with community size, but the growth saturates or slows down for communities larger than a characteristic size. This behaviour is related to the presence of hubs within communities, whose roles differ across categories. Also the community embeddedness of nodes, measured in terms of the fraction of links within their communities, has a characteristic distribution for each category.

Conclusions/Significance

Our findings, verified by the use of two fundamentally different community detection methods, allow for a classification of real networks and pave the way to a realistic modelling of networks'' evolution.     

Dynamic Social Community Detection and Its Applications

Community structure is one of the most commonly observed features of Online Social Networks (OSNs) in reality. The knowledge of this feature is of great advantage: it not only provides helpful insights into developing more efficient social-aware solutions but also promises a wide range of applications enabled by social and mobile networking, such as routing strategies in Mobile Ad Hoc Networks (MANETs) and worm containment in OSNs. Unfortunately, understanding this structure is very challenging, especially in dynamic social networks where social interactions are evolving rapidly. Our work focuses on the following questions: How can we efficiently identify communities in dynamic social networks? How can we adaptively update the network community structure based on its history instead of recomputing from scratch? To this end, we present Quick Community Adaptation (QCA), an adaptive modularity-based framework for not only discovering but also tracing the evolution of network communities in dynamic OSNs. QCA is very fast and efficient in the sense that it adaptively updates and discovers the new community structure based on its history together with the network changes only. This flexible approach makes QCA an ideal framework applicable for analyzing large-scale dynamic social networks due to its lightweight computing-resource requirement. To illustrate the effectiveness of our framework, we extensively test QCA on both synthesized and real-world social networks including Enron, arXiv e-print citation, and Facebook networks. Finally, we demonstrate the applicability of QCA in real applications: (1) A social-aware message forwarding strategy in MANETs, and (2) worm propagation containment in OSNs. Competitive results in comparison with other methods reveal that social-based techniques employing QCA as a community detection core outperform current available methods.     

Community Landscapes: An Integrative Approach to Determine Overlapping Network Module Hierarchy,Identify Key Nodes and Predict Network Dynamics

Background

Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult.

Methodology/Principal Findings

Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence function-based, centrality-type community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoom-in analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics.

Conclusions/Significance

The concept opens a wide range of possibilities to develop new approaches and applications including network routing, classification, comparison and prediction.     

Discovering Preferential Patterns in Sectoral Trade Networks

We analyze the patterns of import/export bilateral relations, with the aim of assessing the relevance and shape of “preferentiality” in countries’ trade decisions. Preferentiality here is defined as the tendency to concentrate trade on one or few partners. With this purpose, we adopt a systemic approach through the use of the tools of complex network analysis. In particular, we apply a pattern detection approach based on community and pseudocommunity analysis, in order to highlight the groups of countries within which most of members’ trade occur. The method is applied to two intra-industry trade networks consisting of 221 countries, relative to the low-tech “Textiles and Textile Articles” and the high-tech “Electronics” sectors for the year 2006, to look at the structure of world trade before the start of the international financial crisis. It turns out that the two networks display some similarities and some differences in preferential trade patterns: they both include few significant communities that define narrow sets of countries trading with each other as preferential destinations markets or supply sources, and they are characterized by the presence of similar hierarchical structures, led by the largest economies. But there are also distinctive features due to the characteristics of the industries examined, in which the organization of production and the destination markets are different. Overall, the extent of preferentiality and partner selection at the sector level confirm the relevance of international trade costs still today, inducing countries to seek the highest efficiency in their trade patterns.     

A comprehensive examination of the network position hypothesis across multiple river metacommunities

The hierarchical branching nature of river networks can have a strong influence on the assembly of freshwater communities. This unique structure has spurred the development of the network position hypothesis (NPH), which states that the strength of different assembly processes depends on the community position in the river network. Specifically, it predicts that 1) headwater communities should be exclusively controlled by the local environment given that they are more isolated and environmentally heterogeneous relative to downstream reaches. In contrast, 2) downstream communities should be regulated by both environmental and dispersal processes due to increased connectivity given their central position in the riverscape. Although intuitive, the NPH has only been evaluated on a few catchments and it is not yet clear whether its predictions are generalizable. To fill this gap, we tested the NPH on river dwelling fishes using an extensive dataset from 28 French catchments. Stream and climatic variables were assembled to characterize environmental conditions and graph theory was applied on river networks to create spatial variables. We tested both predictions using variation partitioning analyses separately for headwater and downstream sites in each catchment. Only 10 catchments supported both predictions, 11 failed to support at least one of them, while in 7 the NPH was partially supported given that spatial variables were also significant for headwater communities. We then assembled a dataset at the catchment scale (e.g. topography, environmental heterogeneity, network connectivity) and applied a classification tree analysis (CTA) to determine which regional property could explain these results. The CTA showed that the NPH was not supported in catchments with high heterogeneity in connectivity among sites. In more homogeneously connected catchments, the NPH was only supported when headwaters were more environmentally heterogeneous than downstream sites. We conclude that the NPH is context dependent even for taxa dispersing exclusively within streams.     

Relative stability of core groups in pollination networks in a biodiversity hotspot over four years

Plants and their pollinators form pollination networks integral to the evolution and persistence of species in communities. Previous studies suggest that pollination network structure remains nested while network composition is highly dynamic. However, little is known about temporal variation in the structure and function of plant-pollinator networks, especially in species-rich communities where the strength of pollinator competition is predicted to be high. Here we quantify temporal variation of pollination networks over four consecutive years in an alpine meadow in the Hengduan Mountains biodiversity hotspot in China. We found that ranked positions and idiosyncratic temperatures of both plants and pollinators were more conservative between consecutive years than in non-consecutive years. Although network compositions exhibited high turnover, generalized core groups--decomposed by a k-core algorithm--were much more stable than peripheral groups. Given the high rate of turnover observed, we suggest that identical plants and pollinators that persist for at least two successive years sustain pollination services at the community level. Our data do not support theoretical predictions of a high proportion of specialized links within species-rich communities. Plants were relatively specialized, exhibiting less variability in pollinator composition at pollinator functional group level than at the species level. Both specialized and generalized plants experienced narrow variation in functional pollinator groups. The dynamic nature of pollination networks in the alpine meadow demonstrates the potential for networks to mitigate the effects of fluctuations in species composition in a high biodiversity area.     

The legacy of transnational lives: Beyond the first generation of Lebanese in Senegal

Definitions of transnationalism are modelled after first generation migrant communities in the west. Through presenting ethnographic detail on the Lebanese community in Senegal, this article applies the concept of transnationalism to the case of a historic South-South migrant community. Second and later generation ethnic groups maintain transnational ties through notions of self-identity and definitions by others, the importance given to the homeland, and political and religious ideologies. Race, geographic location, and changes in the structure of labour markets are factors that encourage continued ties with the country of origin. Furthermore, transnationalism cannot be limited only to sending and receiving countries. Colonial and former colonial powers can determine the destination of migrants, establish economic hierarchies, and offer a tertiary citizenship to transnational migrants in addition to the dual citizenship of country of origin and destination.     

Temporal variability and coherence of euphotic zone bacterial communities over a decade in the Southern California Bight

Time-series are critical to understanding long-term natural variability in the oceans. Bacterial communities in the euphotic zone were investigated for over a decade at the San Pedro Ocean Time-series station (SPOT) off southern California. Community composition was assessed by Automated Ribosomal Intergenic Spacer Analysis (ARISA) and coupled with measurements of oceanographic parameters for the surface ocean (0–5 m) and deep chlorophyll maximum (DCM, average depth ∼30 m). SAR11 and cyanobacterial ecotypes comprised typically more than one-third of the measured community; diversity within both was temporally variable, although a few operational taxonomic units (OTUs) were consistently more abundant. Persistent OTUs, mostly Alphaproteobacteria (SAR11 clade), Actinobacteria and Flavobacteria, tended to be abundant, in contrast to many rarer yet intermittent and ephemeral OTUs. Association networks revealed potential niches for key OTUs from SAR11, cyanobacteria, SAR86 and other common clades on the basis of robust correlations. Resilience was evident by the average communities drifting only slightly as years passed. Average Bray-Curtis similarity between any pair of dates was ∼40%, with a slight decrease over the decade and obvious near-surface seasonality; communities 8–10 years apart were slightly more different than those 1–4 years apart with the highest rate of change at 0–5 m between communities <4 years apart. The surface exhibited more pronounced seasonality than the DCM. Inter-depth Bray-Curtis similarities repeatedly decreased as the water column stratified each summer. Environmental factors were better predictors of shifts in community composition than months or elapsed time alone; yet, the best predictor was community composition at the other depth (that is, 0–5 m versus DCM).     

Consistent estimation of the number of communities via regularized network embedding

The network analysis plays an important role in numerous application domains including biomedicine. Estimation of the number of communities is a fundamental and critical issue in network analysis. Most existing studies assume that the number of communities is known a priori, or lack of rigorous theoretical guarantee on the estimation consistency. In this paper, we propose a regularized network embedding model to simultaneously estimate the community structure and the number of communities in a unified formulation. The proposed model equips network embedding with a novel composite regularization term, which pushes the embedding vector toward its center and pushes similar community centers collapsed with each other. A rigorous theoretical analysis is conducted, establishing asymptotic consistency in terms of community detection and estimation of the number of communities. Extensive numerical experiments have also been conducted on both synthetic networks and brain functional connectivity network, which demonstrate the superior performance of the proposed method compared with existing alternatives.     

Mesoscopic structure conditions the emergence of cooperation on social networks

Background

We study the evolutionary Prisoner''s Dilemma on two social networks substrates obtained from actual relational data.

Methodology/Principal Findings

We find very different cooperation levels on each of them that cannot be easily understood in terms of global statistical properties of both networks. We claim that the result can be understood at the mesoscopic scale, by studying the community structure of the networks. We explain the dependence of the cooperation level on the temptation parameter in terms of the internal structure of the communities and their interconnections. We then test our results on community-structured, specifically designed artificial networks, finding a good agreement with the observations in both real substrates.

Conclusion

Our results support the conclusion that studies of evolutionary games on model networks and their interpretation in terms of global properties may not be sufficient to study specific, real social systems. Further, the study allows us to define new quantitative parameters that summarize the mesoscopic structure of any network. In addition, the community perspective may be helpful to interpret the origin and behavior of existing networks as well as to design structures that show resilient cooperative behavior.     

Dynamics and Control of Diseases in Networks with Community Structure

The dynamics of infectious diseases spread via direct person-to-person transmission (such as influenza, smallpox, HIV/AIDS, etc.) depends on the underlying host contact network. Human contact networks exhibit strong community structure. Understanding how such community structure affects epidemics may provide insights for preventing the spread of disease between communities by changing the structure of the contact network through pharmaceutical or non-pharmaceutical interventions. We use empirical and simulated networks to investigate the spread of disease in networks with community structure. We find that community structure has a major impact on disease dynamics, and we show that in networks with strong community structure, immunization interventions targeted at individuals bridging communities are more effective than those simply targeting highly connected individuals. Because the structure of relevant contact networks is generally not known, and vaccine supply is often limited, there is great need for efficient vaccination algorithms that do not require full knowledge of the network. We developed an algorithm that acts only on locally available network information and is able to quickly identify targets for successful immunization intervention. The algorithm generally outperforms existing algorithms when vaccine supply is limited, particularly in networks with strong community structure. Understanding the spread of infectious diseases and designing optimal control strategies is a major goal of public health. Social networks show marked patterns of community structure, and our results, based on empirical and simulated data, demonstrate that community structure strongly affects disease dynamics. These results have implications for the design of control strategies.     

Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit

In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or, alternatively, of good graph partitions. In most cases, the algorithms maximize a particular objective function, thereby finding the 'right' split into communities. Although a thorough comparison of algorithms is still lacking, there has been an effort to design benchmarks, i.e., random graph models with known community structure against which algorithms can be evaluated. However, popular community detection methods and benchmarks normally assume an implicit notion of community based on clique-like subgraphs, a form of community structure that is not always characteristic of real networks. Specifically, networks that emerge from geometric constraints can have natural non clique-like substructures with large effective diameters, which can be interpreted as long-range communities. In this work, we show that long-range communities escape detection by popular methods, which are blinded by a restricted 'field-of-view' limit, an intrinsic upper scale on the communities they can detect. The field-of-view limit means that long-range communities tend to be overpartitioned. We show how by adopting a dynamical perspective towards community detection [1], [2], in which the evolution of a Markov process on the graph is used as a zooming lens over the structure of the network at all scales, one can detect both clique- or non clique-like communities without imposing an upper scale to the detection. Consequently, the performance of algorithms on inherently low-diameter, clique-like benchmarks may not always be indicative of equally good results in real networks with local, sparser connectivity. We illustrate our ideas with constructive examples and through the analysis of real-world networks from imaging, protein structures and the power grid, where a multiscale structure of non clique-like communities is revealed.     

The Role of Community Mixing Styles in Shaping Epidemic Behaviors in Weighted Networks

The dynamics of infectious diseases that are spread through direct contact have been proven to depend on the strength of community structure or modularity within the underlying network. It has been recently shown that weighted networks with similar modularity values may exhibit different mixing styles regarding the number of connections among communities and their respective weights. However, the effect of mixing style on epidemic behavior was still unclear. In this paper, we simulate the spread of disease within networks with different mixing styles: a dense-weak style (i.e., many edges among the communities with small weights) and a sparse-strong style (i.e., a few edges among the communities with large weights). Simulation results show that, with the same modularity: 1) the mixing style significantly influences the epidemic size, speed, pattern and immunization strategy; 2) the increase of the number of communities amplifies the effect of the mixing style; 3) when the mixing style changes from sparse-strong to dense-weak, there is a ‘saturation point’, after which the epidemic size and pattern become stable. We also provide a mean-field solution of the epidemic threshold and size on weighted community networks with arbitrary external and internal degree distribution. The solution explains the effect of the second moment of the degree distribution, and a symmetric effect of internal and external connections (incl. degree distribution and weight). Our study has both potential significance for designing more accurate metrics for the community structure and exploring diffusion dynamics on metapopulation networks.     

Towards online multiresolution community detection in large-scale networks

The investigation of community structure in networks has aroused great interest in multiple disciplines. One of the challenges is to find local communities from a starting vertex in a network without global information about the entire network. Many existing methods tend to be accurate depending on a priori assumptions of network properties and predefined parameters. In this paper, we introduce a new quality function of local community and present a fast local expansion algorithm for uncovering communities in large-scale networks. The proposed algorithm can detect multiresolution community from a source vertex or communities covering the whole network. Experimental results show that the proposed algorithm is efficient and well-behaved in both real-world and synthetic networks.     

Predicting the effect of competition on secondary plant extinctions in plant–pollinator networks

What are the limitations of models that predict the behavior of an ecological community based on a single type of species interaction? Using plant–pollinator network models as an example, we contrast the predicted vulnerability of a community to secondary extinctions under the assumption of purely mutualistic interactions versus mutualistic and competitive interactions. We find that competition among plant species increases the risk of secondary extinctions and extinction cascades. Simulations over a number of different network structures indicate that this effect is stronger in larger networks, more strongly connected networks and networks with higher plant:pollinator ratios. We conclude that efforts to model plant–pollinator communities will systematically over‐estimate community robustness to species loss if plant competition is ignored. However, because the effect of plant competition depends on network architecture, and because characterization of plant competition is work intensive, we suggest that efforts to account for plant competition in plant–pollinator network models should be focused on large, strongly connected networks with high plant:pollinator ratios.     

藏东南典型暗针叶林不同土壤剖面微生物群落特征

深层土壤中的微生物群落对陆地生态系统养分和能量循环转化过程不可或缺,研究青藏高原典型暗针叶林带土壤微生物群落在土壤垂直剖面的变化特征,对深入认识高寒区域森林生态系统土壤微生物群落构建特征及全球变化影响预测具有重要意义。运用Illumina Miseq高通量测序技术和分子生态网络分析,研究藏东南色季拉山暗针叶林带表层（0-20 cm）和底层土壤（40-60 cm）微生物群落组成及分子生态网络结构。研究结果表明随着土壤深度增加,真菌和细菌的丰富度和Shannon多样性指数显著降低。主坐标分析（PCoA）显示土壤深度显著影响真菌和细菌的群落结构（P < 0.01）。不同微生物种群对土壤深度的响应有显著差异,座囊菌纲（Dothideomycetes）、银耳纲（Tremellomycetes）和拟杆菌门（Bacteroidetes）、变形菌门（Proteobacteria）的相对丰度随剖面加深而显著降低,而古菌根菌纲（Archaeorhizomycetes）和绿弯菌门（Chloroflexi）则显著增加。分子生态网络分析发现,真菌网络以负相关连接为主（占总连接数65%-98%）,而细菌网络以正相关连接为主（69%-75%）,真菌和细菌网络中正相关连接的比例均随剖面加深而增加。底层土壤真菌和细菌网络的平均连接度和平均聚类系数均高于表层土壤,说明微生物网络随土壤深度的增加而变得更复杂。真菌网络的平均路径距离和模块性在底层土壤均大于表层土壤,意味着真菌网络应对环境变化的稳定性随剖面加深而增加,而细菌网络则正相反,在表层土壤的稳定性更强。真菌网络中连接节点的个数随剖面加深而增加,锤舌菌纲（Leotiomycetes）是连接网络模块的关键菌种;在细菌网络中模块枢纽和连接节点则随剖面加深而降低,并且放线菌门、变形菌门等关键种群在分子生态网络中的功能在表层和底层土壤有明显差异。综上所述,藏东南色季拉山暗针叶林带深层土壤中微生物群落特征与表层土壤有显著差别,揭示影响深层土壤微生物网络构建和稳定的关键种群,对深入理解和预测青藏高原森林生态系统对全球变化的响应与反馈有重要意义。