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.     

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.     

Generating Attributed Networks with Communities

In many modern applications data is represented in the form of nodes and their relationships, forming an information network. When nodes are described with a set of attributes we have an attributed network. Nodes and their relationships tend to naturally form into communities or clusters, and discovering these communities is paramount to many applications. Evaluating algorithms or comparing algorithms for automatic discovery of communities requires networks with known structures. Synthetic generators of networks have been proposed for this task but most solely focus on connectivity and their properties and overlook attribute values and the network properties vis-à-vis these attributes. In this paper, we propose a new generator for attributed networks with community structure that dependably follows the properties of real world networks.     

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.     

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.     

The Edge and the Center: Gated Communities and the Discourse of Urban Fear

Across America, middle-class and upper-middle-class gated communities are creating new forms of exclusion and residential segregation, exacerbating social cleavages that already exist (Blakely and Snyder 1997; Higley 1995; Lang and Danielson 1997; Marcuse 1997). While historically secured and gated communities were built in the United States to protect estates and to contain the leisure world of retirees, these urban and suburban developments now target a much broader market, including families with children (Guterson 1992; Lofland 1998). This retreat to secured enclaves with walls, gates, and guards materially and symbolically contradicts American ethos and values, threatens public access to open space, and creates yet another barrier to social interaction, building of social networks, as well as increased tolerance of diverse cultural/ racial/social groups (Davis 1992;Devine 1996;Etzoni 1995; Judd 1995; McKenzie 1994).
In this paper, I explore how the discourse of fear of violence and crime and the search for a secure community by those who live in gated communities in the United States legitimates and rationalizes class-based exclusion strategies and residential segregation. I examine whether residents of cities experiencing increasing cultural diversity are fleeing neighborhoods because they have experienced a "loss of place" and therefore feel unsafe and insecure (Altaian and Low 1992). Some people are responding to this loss by choosing to buy into a defensive space, a walled and guarded community that they can call home, [gated communities, United States, urban fear]     

Finding Influential Spreaders from Human Activity beyond Network Location

Most centralities proposed for identifying influential spreaders on social networks to either spread a message or to stop an epidemic require the full topological information of the network on which spreading occurs. In practice, however, collecting all connections between agents in social networks can be hardly achieved. As a result, such metrics could be difficult to apply to real social networks. Consequently, a new approach for identifying influential people without the explicit network information is demanded in order to provide an efficient immunization or spreading strategy, in a practical sense. In this study, we seek a possible way for finding influential spreaders by using the social mechanisms of how social connections are formed in real networks. We find that a reliable immunization scheme can be achieved by asking people how they interact with each other. From these surveys we find that the probabilistic tendency to connect to a hub has the strongest predictive power for influential spreaders among tested social mechanisms. Our observation also suggests that people who connect different communities is more likely to be an influential spreader when a network has a strong modular structure. Our finding implies that not only the effect of network location but also the behavior of individuals is important to design optimal immunization or spreading schemes.     

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.     

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.     

Rethinking Indigenous Place: Igorot Identity and Locality in the Philippines

Spanish and American colonisers ascribed the identity ‘Igorot’ to the peoples of the northern Philippine mountains, positioning them in the ‘tribal slot’, somewhere between ordinary peasants and ‘backward’ primitives. From this marginal position, contemporary Igorot communities have been comparatively successful in formalising their entitlements to land and resources in their dealings with the Philippine State. This success depends on a discourse tying indigenous or ‘tribal’ culture to particular places. Colonial and, now, local anthropology has been recruited to this process through the mapping of community boundaries. This has allowed groups to secure official status as ‘cultural communities' and gain legal recognition of their ancestral domains. Ironically, even as ancestral domains are recognised, the municipalities that hold such domains have ceased to be bounded containers for Igorot localities, if they ever were. Participation in global indigenous networks, circular migration, and ongoing relations with emigrants overseas blur the spatial, temporal, and social boundaries of Igorot communities. Transnational flows of people, information, and value are recruited to support the essentialised versions of indigenous identity necessary for negotiations with the state. Here, I show how the specific history of the Igorot ‘tribal slot’ enables communities to perform essentialised indigeneity and simultaneously enact highly translocal modes of cultural reproduction.     

Fast Fragmentation of Networks Using Module-Based Attacks

In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from a practical point of view. In this contribution, we present a module-based method to efficiently fragment complex networks. The procedure firstly identifies topological communities through which the network can be represented using a well established heuristic algorithm of community finding. Then only the nodes that participate of inter-community links are removed in descending order of their betweenness centrality. We illustrate the method by applying it to a variety of examples in the social, infrastructure, and biological fields. It is shown that the module-based approach always outperforms targeted attacks to vertices based on node degree or betweenness centrality rankings, with gains in efficiency strongly related to the modularity of the network. Remarkably, in the US power grid case, by deleting 3% of the nodes, the proposed method breaks the original network in fragments which are twenty times smaller in size than the fragments left by betweenness-based attack.     

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.     

Keystone species and food webs

Different species are of different importance in maintaining ecosystem functions in natural communities. Quantitative approaches are needed to identify unusually important or influential, ‘keystone’ species particularly for conservation purposes. Since the importance of some species may largely be the consequence of their rich interaction structure, one possible quantitative approach to identify the most influential species is to study their position in the network of interspecific interactions. In this paper, I discuss the role of network analysis (and centrality indices in particular) in this process and present a new and simple approach to characterizing the interaction structures of each species in a complex network. Understanding the linkage between structure and dynamics is a condition to test the results of topological studies, I briefly overview our current knowledge on this issue. The study of key nodes in networks has become an increasingly general interest in several disciplines: I will discuss some parallels. Finally, I will argue that conservation biology needs to devote more attention to identify and conserve keystone species and relatively less attention to rarity.     

The risks we dread: a social circle account

What makes some risks dreadful? We propose that people are particularly sensitive to threats that could kill the number of people that is similar to the size of a typical human social circle. Although there is some variability in reported sizes of social circles, active contact rarely seems to be maintained with more than about 100 people. The loss of this immediate social group may have had survival consequences in the past and still causes great distress to people today. Therefore we hypothesize that risks that threaten a much larger number of people (e.g., 1000) will not be dreaded more than those that threaten to kill “only” the number of people typical for social circles. We found support for this hypothesis in 9 experiments using different risk scenarios, measurements of fear, and samples from different countries. Fear of risks killing 100 people was higher than fear of risks killing 10 people, but there was no difference in fear of risks killing 100 or 1000 people (Experiments 1–4, 7–9). Also in support of the hypothesis, the median number of deaths that would cause maximum level of fear was 100 (Experiments 5 and 6). These results are not a consequence of lack of differentiation between the numbers 100 and 1000 (Experiments 7 and 8), and are different from the phenomenon of “psychophysical numbing” that occurs in the context of altruistic behavior towards members of other communities rather than in the context of threat to one''s own community (Experiment 9). We discuss several possible explanations of these findings. Our results stress the importance of considering social environments when studying people''s understanding of and reactions to risks.     

Structure–stability relationships in networks combining mutualistic and antagonistic interactions

The relationship between the structure of ecological networks and community stability has been studied for decades. Recent developments highlighted that this relationship depended on whether interactions were antagonistic or mutualistic. Different structures promoting stability in different types of ecological networks, i.e. mutualistic or antagonistic, have been pointed out. However, these findings come from studies considering mutualistic and antagonistic interactions separately whereas we know that species are part of both types of networks simultaneously. Understanding the relationship between network structure and community stability, when mutualistic and antagonistic interactions are merged in a single network, thus appears as the next challenge to improve our understanding of the dynamics of natural communities. Using a theoretical approach, we test whether the structural characteristics known to promote stability in networks made of a single interaction type still hold for network merging mutualistic and antagonistic interactions. We show that the effects of diversity and connectance remain unchanged. But the effects of nestedness and modularity are strongly weakened in networks combining mutualistic and antagonistic interactions. By challenging the stabilizing mechanisms proposed for networks with a single interaction type, our study calls for new measures of structure for networks that integrate the diversity of interaction.     

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.     

Top‐down network analysis characterizes hidden termite–termite interactions

The analysis of ecological networks is generally bottom‐up, where networks are established by observing interactions between individuals. Emergent network properties have been indicated to reflect the dominant mode of interactions in communities that might be mutualistic (e.g., pollination) or antagonistic (e.g., host–parasitoid communities). Many ecological communities, however, comprise species interactions that are difficult to observe directly. Here, we propose that a comparison of the emergent properties from detail‐rich reference communities with known modes of interaction can inform our understanding of detail‐sparse focal communities. With this top‐down approach, we consider patterns of coexistence between termite species that live as guests in mounds built by other host termite species as a case in point. Termite societies are extremely sensitive to perturbations, which precludes determining the nature of their interactions through direct observations. We perform a literature review to construct two networks representing termite mound cohabitation in a Brazilian savanna and in the tropical forest of Cameroon. We contrast the properties of these cohabitation networks with a total of 197 geographically diverse mutualistic plant–pollinator and antagonistic host–parasitoid networks. We analyze network properties for the networks, perform a principal components analysis (PCA), and compute the Mahalanobis distance of the termite networks to the cloud of mutualistic and antagonistic networks to assess the extent to which the termite networks overlap with the properties of the reference networks. Both termite networks overlap more closely with the mutualistic plant–pollinator communities than the antagonistic host–parasitoid communities, although the Brazilian community overlap with mutualistic communities is stronger. The analysis raises the hypothesis that termite–termite cohabitation networks may be overall mutualistic. More broadly, this work provides support for the argument that cryptic communities may be analyzed via comparison to well‐characterized communities.     

Network structural properties mediate the stability of mutualistic communities

Key advances are being made on the structures of predator–prey food webs and competitive communities that enhance their stability, but little attention has been given to such complexity–stability relationships for mutualistic communities. We show, by way of theoretical analyses with empirically informed parameters, that structural properties can alter the stability of mutualistic communities characterized by nonlinear functional responses among the interacting species. Specifically, community resilience is enhanced by increasing community size (species diversity) and the number of species interactions (connectivity), and through strong, symmetric interaction strengths of highly nested networks. As a result, mutualistic communities show largely positive complexity–stability relationships, in opposition to the standard paradox. Thus, contrary to the commonly-held belief that mutualism's positive feedback destabilizes food webs, our results suggest that interplay between the structure and function of ecological networks in general, and consideration of mutualistic interactions in particular, may be key to understanding complexity–stability relationships of biological communities as a whole.