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.     

DyCoNet: A Gephi Plugin for Community Detection in Dynamic Complex Networks

Community structure detection has proven to be important in revealing the underlying organisation of complex networks. While most current analyses focus on static networks, the detection of communities in dynamic data is both challenging and timely. An analysis and visualisation procedure for dynamic networks is presented here, which identifies communities and sub-communities that persist across multiple network snapshots. An existing method for community detection in dynamic networks is adapted, extended, and implemented. We demonstrate the applicability of this method to detect communities in networks where individuals tend not to change their community affiliation very frequently. When stability of communities cannot be assumed, we show that the sub-community model may be a better alternative. This is illustrated through test cases of social and biological networks. A plugin for Gephi, an open-source software program used for graph visualisation and manipulation, named “DyCoNet”, was created to execute the algorithm and is freely available from https://github.com/juliemkauffman/DyCoNet.     

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.     

基于复杂网络的长三角城市对外服务群落结构研究

城市群已成为国家参与全球竞争与国际分工的重要空间载体,其空间组织形式正从个体城市集聚、等级性的中心地结构向多中心、嵌套式的群落结构演变。为刻画长三角地区城市在不同要素层面下形成的多层次群落结构及其状态,借助复杂网络分析工具,从城市群落的节点特征、垂直和水平结构、不同群落结构间的相互关联三方面实证分析长三角地区3类(生产性、生活性、公共性)对外服务流的网络结构特征。研究显示:1)长三角城市节点服务功能分化,节点层级性分异显著,生产和生活性服务网络的节点规模呈"长尾"分布,公共性服务网络的节点规模相对均衡;2)垂直结构上,3类对外服务网络的网络密度、网络效率、流量占比和空间分布各不相同;水平结构上,初步形成对外服务网络的专业化分工格局,部分城市突破区域界线,呈跨地域集聚组团的态势。3)较强的结构关联性存在于生产性和生活性对外服务网络之间,两者在中低度值的城市节点上具有一致性,呈联动发展格局;公共性对外服务网络与前两者的节点度值分异较大,促进了整体群落服务功能结构的丰富和完善。基于复杂网络的群落研究可以从多维结构的分析中寻求城市群落的分工协作和共生,为当前多核心、网络化的城市空间组织与规划提供科学参考。     

Damming river shapes distinct patterns and processes of planktonic bacterial and microeukaryotic communities

Planktonic bacterial and microeukaryotic communities play important roles in biogeochemical cycles, but their biogeographic patterns and community assembly processes in large damming rivers still remain unclear. In this study, 16S rRNA and 18S rRNA coding genes were used for sample sequencing analysis of planktonic bacterial and microeukaryotic communities in the upper Yangtze River. The upper Yangtze River was divided into dam-affected zones and river zones based on the influence of dams. The results showed that there were significant differences in the bacterial and microeukaryotic communities between the two zones and that dams significantly reduced the α-diversity of the bacterial communities. Co-occurrence network analysis indicated that networks in the river zone were denser than those in the dam-affected zone. The relationships among species in bacterial networks were more complex than those in microeukaryotic networks. Dispersal limitation and ecological drift were the main processes influencing planktonic bacterial and microeukaryotic communities in the dam-affected zone respectively, whereas the role of deterministic processes increased in the river zone. Anthropogenic activities and hydraulic conditions affected suspended sediment and controlled microbial diversity in the river zone. These results suggest that dams impact planktonic bacteria more strongly than planktonic microeukaryotes, indicating that the distribution patterns and processes of the bacterial and microeukaryotic communities in large rivers are significantly different.     

Microbial biogeography of drinking water: patterns in phylogenetic diversity across space and time

In this study, we collected water from different locations in 32 drinking water distribution networks in the Netherlands and analysed the spatial and temporal variation in microbial community composition by high‐throughput sequencing of 16S rRNA gene amplicons. We observed that microbial community compositions of raw source and processed water were very different for each distribution network sampled. In each network, major differences in community compositions were observed between raw and processed water, although community structures of processed water did not differ substantially from end‐point tap water. End‐point water samples within the same distribution network revealed very similar community structures. Network‐specific communities were shown to be surprisingly stable in time. Biofilm communities sampled from domestic water metres varied distinctly between households and showed no resemblance to planktonic communities within the same distribution networks. Our findings demonstrate that high‐throughput sequencing provides a powerful and sensitive tool to probe microbial community composition in drinking water distribution systems. Furthermore, this approach can be used to quantitatively compare the microbial communities to match end‐point water samples to specific distribution networks. Insight in the ecology of drinking water distribution systems will facilitate the development of effective control strategies that will ensure safe and high‐quality drinking water.     

Mapping and characterization of LCA networks

Purpose

The aims of this study were to provide an up-to-date overview of global, regional and local networks supporting life cycle thinking and to characterize them according to their structure and activities.

Methods

Following a tentative life cycle assessment (LCA) network definition, a mapping was performed based on (1) a literature search, (2) a web search and (3) an inquiry to stakeholders distributed via the two largest LCA fora. Networks were characterized based on responses from a survey.

Results and discussion

We identified 100 networks, of which 29 fulfilled all six criteria composing our tentative network definition (the remaining fulfilled four to five criteria). The networks are mainly located in Europe and the USA, whilst Africa, the Middle East and Central Asia are less covered regions. The survey results (from 25 network responses) indicate that LCA networks appear to be primarily small- to medium-sized (<100 members) and to include a large proportion of academia and industries, including small- and medium-sized enterprises, with much less involvement of authorities and non-governmental organisations. Their major activities relate to knowledge sharing and communication, support of case studies, and development of life cycle inventories and impact assessment methods. Networks in developing economies have different structures and activities than networks in developed economies and, for instance, more frequently have members from non-governmental organisations. Globally, an increasing trend in the formation of LCA networks over time is observed, which tends to correlate with the number of LCA scientific publications over the same time period. Continental distributions of networks also show a correlation with the number of LCA publications from the same region.

Conclusions

The provided list of LCA networks is currently the most comprehensive, publicly available mapping. We believe that the results of this mapping can serve as a basis for deciding where priorities should be set to increase the dissemination and development of LCA worldwide. In this aim, we also advocate the creation of an online, regularly updated database of LCA networks supplemented by an online platform that could facilitate network communication and knowledge sharing.     

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.     

Followers Are Not Enough: A Multifaceted Approach to Community Detection in Online Social Networks

In online social media networks, individuals often have hundreds or even thousands of connections, which link these users not only to friends, associates, and colleagues, but also to news outlets, celebrities, and organizations. In these complex social networks, a ‘community’ as studied in the social network literature, can have very different meaning depending on the property of the network under study. Taking into account the multifaceted nature of these networks, we claim that community detection in online social networks should also be multifaceted in order to capture all of the different and valuable viewpoints of ‘community.’ In this paper we focus on three types of communities beyond follower-based structural communities: activity-based, topic-based, and interaction-based. We analyze a Twitter dataset using three different weightings of the structural network meant to highlight these three community types, and then infer the communities associated with these weightings. We show that interesting insights can be obtained about the complex community structure present in social networks by studying when and how these four community types give rise to similar as well as completely distinct community structure.     

Place-Based Attributes Predict Community Membership in a Mobile Phone Communication Network

Social networks can be organized into communities of closely connected nodes, a property known as modularity. Because diseases, information, and behaviors spread faster within communities than between communities, understanding modularity has broad implications for public policy, epidemiology and the social sciences. Explanations for community formation in social networks often incorporate the attributes of individual people, such as gender, ethnicity or shared activities. High modularity is also a property of large-scale social networks, where each node represents a population of individuals at a location, such as call flow between mobile phone towers. However, whether or not place-based attributes, including land cover and economic activity, can predict community membership for network nodes in large-scale networks remains unknown. We describe the pattern of modularity in a mobile phone communication network in the Dominican Republic, and use a linear discriminant analysis (LDA) to determine whether geographic context can explain community membership. Our results demonstrate that place-based attributes, including sugar cane production, urbanization, distance to the nearest airport, and wealth, correctly predicted community membership for over 70% of mobile phone towers. We observed a strongly positive correlation (r = 0.97) between the modularity score and the predictive ability of the LDA, suggesting that place-based attributes can accurately represent the processes driving modularity. In the absence of social network data, the methods we present can be used to predict community membership over large scales using solely place-based attributes.     

垂叶榕榕小蜂群落及种间互作网络季节动态

群落中的物种相互作用构成了复杂的生态网络。有关物种的数量和组成的季节性动态变化已有较多的研究, 但是对于生态网络的动态变化知之甚少。揭示生态网络的动态变化对于理解群落的稳定性以及群落的动态变化过程和机理具有重要意义。本研究以垂叶榕(Ficus benjamina)榕小蜂群落为研究对象, 分别在西双版纳的干季和雨季采集了榕小蜂的种类和数量信息。比较了两个季节榕小蜂群落的动态变化以及共存网络的参数(例如网路直径、连接数、嵌套性和群落矩阵温度)变化。结果显示: 雨季榕果内传粉榕小蜂Eupristina koningsbergeri所占比例高于干季, 传粉榕小蜂的种群数量也高于干季, 而在干季非传粉榕小蜂的种类增加(干季15种小蜂, 雨季14种)。从榕树-传粉榕小蜂互利共生系统的适合度来看, 干季非传粉小蜂的增加对传粉榕小蜂和榕树的适合度是不利的。在干季, 共存网络物种间的连接数(干季0.95, 雨季0.47)多于雨季, 群落矩阵温度(干季23.24, 雨季2.64)也显著高于雨季。表明干季榕小蜂群落组成及种间关系较雨季更为复杂而多样, 高的矩阵温度暗示群落受到的干扰更大。     

The overlapping community structure of structural brain network in young healthy individuals

Community structure is a universal and significant feature of many complex networks in biology, society, and economics. Community structure has also been revealed in human brain structural and functional networks in previous studies. However, communities overlap and share many edges and nodes. Uncovering the overlapping community structure of complex networks remains largely unknown in human brain networks. Here, using regional gray matter volume, we investigated the structural brain network among 90 brain regions (according to a predefined anatomical atlas) in 462 young, healthy individuals. Overlapped nodes between communities were defined by assuming that nodes (brain regions) can belong to more than one community. We demonstrated that 90 brain regions were organized into 5 overlapping communities associated with several well-known brain systems, such as the auditory/language, visuospatial, emotion, decision-making, social, control of action, memory/learning, and visual systems. The overlapped nodes were mostly involved in an inferior-posterior pattern and were primarily related to auditory and visual perception. The overlapped nodes were mainly attributed to brain regions with higher node degrees and nodal efficiency and played a pivotal role in the flow of information through the structural brain network. Our results revealed fuzzy boundaries between communities by identifying overlapped nodes and provided new insights into the understanding of the relationship between the structure and function of the human brain. This study provides the first report of the overlapping community structure of the structural network of the human brain.     

The Functional Connectome of Speech Control

In the past few years, several studies have been directed to understanding the complexity of functional interactions between different brain regions during various human behaviors. Among these, neuroimaging research installed the notion that speech and language require an orchestration of brain regions for comprehension, planning, and integration of a heard sound with a spoken word. However, these studies have been largely limited to mapping the neural correlates of separate speech elements and examining distinct cortical or subcortical circuits involved in different aspects of speech control. As a result, the complexity of the brain network machinery controlling speech and language remained largely unknown. Using graph theoretical analysis of functional MRI (fMRI) data in healthy subjects, we quantified the large-scale speech network topology by constructing functional brain networks of increasing hierarchy from the resting state to motor output of meaningless syllables to complex production of real-life speech as well as compared to non-speech-related sequential finger tapping and pure tone discrimination networks. We identified a segregated network of highly connected local neural communities (hubs) in the primary sensorimotor and parietal regions, which formed a commonly shared core hub network across the examined conditions, with the left area 4p playing an important role in speech network organization. These sensorimotor core hubs exhibited features of flexible hubs based on their participation in several functional domains across different networks and ability to adaptively switch long-range functional connectivity depending on task content, resulting in a distinct community structure of each examined network. Specifically, compared to other tasks, speech production was characterized by the formation of six distinct neural communities with specialized recruitment of the prefrontal cortex, insula, putamen, and thalamus, which collectively forged the formation of the functional speech connectome. In addition, the observed capacity of the primary sensorimotor cortex to exhibit operational heterogeneity challenged the established concept of unimodality of this region.     

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.     

Convergent evolution of modularity in metabolic networks through different community structures

ABSTRACT: BACKGROUND: It has been reported that the modularity of metabolic networks of bacteria is closely relatedto the variability of their living habitats. However, given the dependency of the modularityscore on the community structure, it remains unknown whether organisms achieve certainmodularity via similar or different community structures. RESULTS: In this work, we studied the relationship between similarities in modularity scores andsimilarities in community structures of the metabolic networks of 1021 species. Bothsimilarities are then compared against the genetic distances. We revisited the associationbetween modularity and variability of the microbial living environments and extended theanalysis to other aspects of their life style such as temperature and oxygen requirements. Wealso tested both topological and biological intuition of the community structures identifiedand investigated the extent of their conservation with respect to the taxomony. CONCLUSIONS: We find that similar modularities are realized by different community structures. We findthat such convergent evolution of modularity is closely associated with the number of(distinct) enzymes in the organism's metabolome, a consequence of different life styles ofthe species. We find that the order of modularity is the same as the order of the number ofthe enzymes under the classification based on the temperature preference but not on theoxygen requirement. Besides, inspection of modularity-based communities reveals thatthese communities are graph-theoretically meaningful yet not reflective of specificbiological functions. From an evolutionary perspective, we find that the communitystructures are conserved only at the level of kingdoms. Our results call for moreinvestigation into the interplay between evolution and modularity: how evolution shapesmodularity, and how modularity affects evolution (mainly in terms of fitness andevolvability). Further, our results call for exploring new measures of modularity andnetwork communities that better correspond to functional categorizations.     

Netgram: Visualizing Communities in Evolving Networks

Real-world complex networks are dynamic in nature and change over time. The change is usually observed in the interactions within the network over time. Complex networks exhibit community like structures. A key feature of the dynamics of complex networks is the evolution of communities over time. Several methods have been proposed to detect and track the evolution of these groups over time. However, there is no generic tool which visualizes all the aspects of group evolution in dynamic networks including birth, death, splitting, merging, expansion, shrinkage and continuation of groups. In this paper, we propose Netgram: a tool for visualizing evolution of communities in time-evolving graphs. Netgram maintains evolution of communities over 2 consecutive time-stamps in tables which are used to create a query database using the sql outer-join operation. It uses a line-based visualization technique which adheres to certain design principles and aesthetic guidelines. Netgram uses a greedy solution to order the initial community information provided by the evolutionary clustering technique such that we have fewer line cross-overs in the visualization. This makes it easier to track the progress of individual communities in time evolving graphs. Netgram is a generic toolkit which can be used with any evolutionary community detection algorithm as illustrated in our experiments. We use Netgram for visualization of topic evolution in the NIPS conference over a period of 11 years and observe the emergence and merging of several disciplines in the field of information processing systems.     

Community Size Effects on Epidemic Spreading in Multiplex Social Networks

The dynamical process of epidemic spreading has drawn much attention of the complex network community. In the network paradigm, diseases spread from one person to another through the social ties amongst the population. There are a variety of factors that govern the processes of disease spreading on the networks. A common but not negligible factor is people’s reaction to the outbreak of epidemics. Such reaction can be related information dissemination or self-protection. In this work, we explore the interactions between disease spreading and population response in terms of information diffusion and individuals’ alertness. We model the system by mapping multiplex networks into two-layer networks and incorporating individuals’ risk awareness, on the assumption that their response to the disease spreading depends on the size of the community they belong to. By comparing the final incidence of diseases in multiplex networks, we find that there is considerable mitigation of diseases spreading for full phase of spreading speed when individuals’ protection responses are introduced. Interestingly, the degree of community overlap between the two layers is found to be critical factor that affects the final incidence. We also analyze the consequences of the epidemic incidence in communities with different sizes and the impacts of community overlap between two layers. Specifically, as the diseases information makes individuals alert and take measures to prevent the diseases, the effective protection is more striking in small community. These phenomena can be explained by the multiplexity of the networked system and the competition between two spreading processes.     

A Developmental Systems Perspective on Epistasis: Computational Exploration of Mutational Interactions in Model Developmental Regulatory Networks

The way in which the information contained in genotypes is translated into complex phenotypic traits (i.e. embryonic expression patterns) depends on its decoding by a multilayered hierarchy of biomolecular systems (regulatory networks). Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/− feedback) and associated control parameters, resulting in characteristic variational constraints. This process can be conceptualized as a mapping issue, and in the context of highly-dimensional genotype-phenotype mappings (GPMs) epistatic events have been shown to be ubiquitous, manifested in non-linear correspondences between changes in the genotype and their phenotypic effects. In this study I concentrate on epistatic phenomena pervading levels of biological organization above the genetic material, more specifically the realm of molecular networks. At this level, systems approaches to studying GPMs are specially suitable to shed light on the mechanistic basis of epistatic phenomena. To this aim, I constructed and analyzed ensembles of highly-modular (fully interconnected) networks with distinctive topologies, each displaying dynamic behaviors that were categorized as either arbitrary or functional according to early patterning processes in the Drosophila embryo. Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models. My in silico mutational experiments show that: 1) the average fitness decay tendency to successively accumulated mutations in ensembles of functional networks indicates the prevalence of positive epistasis, whereas in ensembles of arbitrary networks negative epistasis is the dominant tendency; and 2) the evaluation of epistatic coefficients of diverse interaction orders indicates that, both positive and negative epistasis are more prevalent in functional networks than in arbitrary ones. Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks.