Based on the definition of local spectral subspace, we propose a novel approach called LOSP for local overlapping community detection. Instead of using the invariant subspace spanned by the dominant eigenvectors of the entire network, we run the power method for a few steps to approximate the leading eigenvectors that depict the embedding of the local neighborhood structure around seeds of interest. We then seek a sparse approximate indicator vector in the local spectral subspace spanned by these vectors such that the seeds are in its support.
We evaluate LOSP on five large real world networks across various domains with labeled ground-truth communities and compare the results with the state-of-the-art community detection approaches. LOSP identifies the members of a target community with high accuracy from very few seed members, and outperforms the local Heat Kernel or PageRank diffusions as well as the global baselines.
Two candidate definitions of the local spectral subspace are analyzed, and different community scoring functions for determining the community boundary, including two new metrics, are thoroughly evaluated. The structural properties of different seed sets and the impact of the seed set size are discussed. We observe low degree seeds behave better, and LOSP is robust even when started from a single random seed.
Using LOSP as a subroutine and starting from each ego connected component, we try the harder yet significant task of identifying all communities a single vertex is in. Experiments show that the proposed method achieves high F1 measures on the detected multiple local overlapping communities containing the seed vertex.
Detection of non-overlapping and overlapping communities are essentially the same problem. However, current algorithms focus either on finding overlapping or non-overlapping communities. We present a generalized framework that can identify both non-overlapping and overlapping communities, without any prior input about the network or its community distribution. To do so, we introduce a vertex-based metric, GenPerm, that quantifies by how much a vertex belongs to each of its constituent communities. Our community detection algorithm is based on maximizing the GenPerm over all the vertices in the…
We define an approach to identify overlapping communities in multiplex networks, extending the popular clique percolation method for simple graphs. The extension requires to rethink the basic concepts on which the clique percolation algorithm is based, including cliques and clique adjacency, to allow the presence of multiple types of edges.
We propose that hypergraphs can be used to model social networks with overlapping communities. The nodes of the hypergraphs represent the communities. The hyperlinks of the hypergraphs denote the individuals who may participate in multiple communities. The hypergraphs are not easy to analyze, however, the line graphs of hypergraphs are simple graphs or weighted graphs, so that the network theory can be applied. We define the overlapping depth $k$ of an individual by the number of communities that overlap in that individual, and we prove that the minimum adjacency eigenvalue of the correspondin…
Usually the boundary of a community in a network is drawn between nodes and thus crosses its outgoing links. If we construct overlapping communities by applying the link-clustering approach nodes and links interchange their roles. Therefore, boundaries must drawn through the nodes shared by two or more communities. For the purpose of community evaluation we define a conductance of boundary nodes of overlapping communities analogously to the graph conductance of boundary-crossing links used to partition a graph into disjoint communities. We show that conductance of boundary nodes (or normalised…
Community structure is a typical property of many real-world networks, and has become a key to understand the dynamics of the networked systems. In these networks most nodes apparently lie in a community while there often exists a few nodes straddling several communities. An ideal algorithm for community detection is preferable which can identify the overlapping communities in such networks. To represent an overlapping division we develop a encoding schema composed of two segments, the first one represents a disjoint partition and the second one represents a extension of the partition that all…
We present NECTAR, a community detection algorithm that generalizes Louvain method's local search heuristic for overlapping community structures. NECTAR chooses dynamically which objective function to optimize based on the network on which it is invoked. Our experimental evaluation on both synthetic benchmark graphs and real-world networks, based on ground-truth communities, shows that NECTAR provides excellent results as compared with state of the art community detection algorithms.
Complex networks can be typically broken down into groups or modules. Discovering this "community structure" is an important step in studying the large-scale structure of networks. Many algorithms have been proposed for community detection and benchmarks have been created to evaluate their performance. Typically algorithms for community detection either partition the graph (non-overlapping communities) or find node covers (overlapping communities). In this paper, we propose a particularly simple semi-supervised learning algorithm for finding out communities. In essence, given the community inf…
Detecting community structures in social networks has gained considerable attention in recent years. However, lack of prior knowledge about the number of communities, and their overlapping nature have made community detection a challenging problem. Moreover, many of the existing methods only consider static networks, while most of real world networks are dynamic and evolve over time. Hence, finding consistent overlapping communities in dynamic networks without any prior knowledge about the number of communities is still an interesting open research problem. In this paper, we present an overlap…
Network communities represent mesoscopic structure for understanding the organization of real-world networks, where nodes often belong to multiple communities and form overlapping community structure in the network. Due to non-triviality in finding the exact boundary of such overlapping communities, this problem has become challenging, and therefore huge effort has been devoted to detect overlapping communities from the network. In this paper, we present PVOC (Permanence based Vertex-replication algorithm for Overlapping Community detection), a two-stage framework to detect overlapping communi…
In some social and biological networks, the majority of nodes belong to multiple communities. It has recently been shown that a number of the algorithms that are designed to detect overlapping communities do not perform well in such highly overlapping settings. Here, we consider one class of these algorithms, those which optimize a local fitness measure, typically by using a greedy heuristic to expand a seed into a community. We perform synthetic benchmarks which indicate that an appropriate seeding strategy becomes increasingly important as the extent of community overlap increases. We find t…
Networks commonly exhibit a community structure, whereby groups of vertices are more densely connected to each other than to other vertices. Often these communities overlap, such that each vertex may occur in more than one community. However, two distinct types of overlapping are possible: crisp (where each vertex belongs fully to each community of which it is a member) and fuzzy (where each vertex belongs to each community to a different extent). We investigate the effects of the fuzziness of community overlap. We find that it has a strong effect on the performance of community detection meth…
We propose an algorithm for finding overlapping community structure in very large networks. The algorithm is based on the label propagation technique of Raghavan, Albert, and Kumara, but is able to detect communities that overlap. Like the original algorithm, vertices have labels that propagate between neighbouring vertices so that members of a community reach a consensus on their community membership. Our main contribution is to extend the label and propagation step to include information about more than one community: each vertex can now belong to up to v communities, where v is the paramete…
The conventional notion of community that favors a high ratio of internal edges to outbound edges becomes invalid when each vertex participates in multiple communities. Such a behavior is commonplace in social networks. The significant overlaps among communities make most existing community detection algorithms ineffective. The lack of effective and efficient tools resulted in very few empirical studies on large-scale detection and analyses of overlapping community structure in real social networks. We developed recently a scalable and accurate method called the Partial Community Merger Algori…
Modern networks are of huge sizes as well as high dynamics, which challenges the efficiency of community detection algorithms. In this paper, we study the problem of overlapping community detection on distributed and dynamic graphs. Given a distributed, undirected and unweighted graph, the goal is to detect overlapping communities incrementally as the graph is dynamically changing. We propose an efficient algorithm, called \textit{randomized Speaker-Listener Label Propagation Algorithm} (rSLPA), based on the \textit{Speaker-Listener Label Propagation Algorithm} (SLPA) by relaxing the probabili…
We propose an algorithm for detecting communities of links in networks which uses local information, is based on a new evaluation function, and allows for pervasive overlaps of communities. The complexity of the clustering task requires the application of a memetic algorithm that combines probabilistic evolutionary strategies with deterministic local searches. In Part 2 we will present results of experiments with with citation networks.
Given a set ${\cal AL}$ of community detection algorithms and a graph $G$ as inputs, we propose two ensemble methods $\mathtt{EnDisCO}$ and $\mathtt{MeDOC}$ that (respectively) identify disjoint and overlapping communities in $G$. $\mathtt{EnDisCO}$ transforms a graph into a latent feature space by leveraging multiple base solutions and discovers disjoint community structure. $\mathtt{MeDOC}$ groups similar base communities into a meta-community and detects both disjoint and overlapping community structures. Experiments are conducted at different scales on both synthetically generated networks…
Overlap is one of the characteristics of social networks, in which a person may belong to more than one social group. For this reason, discovering overlapping structures is necessary for realistic social analysis. In this paper, we present a novel, general framework to detect and analyze both individual overlapping nodes and entire communities. In this framework, nodes exchange labels according to dynamic interaction rules. A specific implementation called Speaker-listener Label Propagation Algorithm (SLPA1) demonstrates an excellent performance in identifying both overlapping nodes and overla…
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of communities or clusters is used to illustrate how a clique graph may be exploited. In particular a benchmark network is shown where clique graphs find the overlapping communities accurately while vertex partition methods fail.
Communities are subsets of a network that are densely connected inside and share only few connections to the rest of the network. The aim of this research is the development and evaluation of an efficient algorithm for detection of overlapping, fuzzy communities. The algorithm gets as input some members of each community that we aim to discover. We call these members seed nodes. The algorithm then propagates this information by using random walks that start at non-seed nodes and end as they reach a seed node. The probability that a random walk starting at a non-seed node $v$ ends at a seed nod…
Most existing approaches for community detection require complete information of the graph in a specific scale, which is impractical for many social networks. We propose a novel algorithm that does not embrace the universal approach but instead of trying to focus on local social ties and modeling multi-scales of social interactions occurring in those networks. Our method for the first time optimizes the topological entropy of a network and uncovers communities through a novel dynamic system converging to a local minimum by simply updating the membership vector with very low computational compl…
We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism accounts for the evolution of the internal link structure of a single community, and the second mechanism coordinates the growth of multiple overlapping communities. The first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates. We demonstrate that this simple m…
Algorithms for detecting communities in complex networks are generally unsupervised, relying solely on the structure of the network. However, these methods can often fail to uncover meaningful groupings that reflect the underlying communities in the data, particularly when those structures are highly overlapping. One way to improve the usefulness of these algorithms is by incorporating additional background information, which can be used as a source of constraints to direct the community detection process. In this work, we explore the potential of semi-supervised strategies to improve algorith…
Multiplex networks are a representation of real-world complex systems as a set of entities (i.e. nodes) connected via different types of connections (i.e. layers). The observed connections in these networks may not be complete and the link prediction task is about locating the missing links across layers. Here, the main challenge is about collecting relevant evidence from different layers to assist the link prediction task. It is known that co-membership in communities increases the likelihood of connectivity between nodes. We discuss that co-membership in the communities of the similar layers…
Community structure is one of the most prominent features of complex networks. Community structure detection is of great importance to provide insights into the network structure and functionalities. Most proposals focus on static networks. However, finding communities in a dynamic network is even more challenging, especially when communities overlap with each other. In this article , we present an online algorithm, called OLCPM, based on clique percolation and label propagation methods. OLCPM can detect overlapping communities and works on temporal networks with a fine granularity. By locally…
We present a new online algorithm for detecting overlapping communities. The main ingredients are a modification of an online k-means algorithm and a new approach to modelling overlap in communities. An evaluation on large benchmark graphs shows that the quality of discovered communities compares favorably to several methods in the recent literature, while the running time is significantly improved.
Complex networks considering both positive and negative links have gained considerable attention during the past several years. Community detection is one of the main challenges for complex network analysis. Most of the existing algorithms for community detection in a signed network aim at providing a hard-partition of the network where any node should belong to a community or not. However, they cannot detect overlapping communities where a node is allowed to belong to multiple communities. The overlapping communities widely exist in many real world networks. In this paper, we propose a signed…
A network has a non-overlapping community structure if the nodes of the network can be partitioned into disjoint sets such that each node in a set is densely connected to other nodes inside the set and sparsely connected to the nodes out- side it. There are many metrics to validate the efficacy of such a structure, such as clustering coefficient, betweenness, centrality, modularity and like-mindedness. Many methods have been proposed to optimize some of these metrics, but none of these works well on the recently introduced metric like-mindedness. To solve this problem, we propose a be- haviora…
Communities commonly overlap in real-world networks. This is a motivation to develop overlapping community detection methods, because methods for non-overlapping communities may not perform well. However, deterioration mechanism of the detection methods used for non-overlapping communities have rarely been investigated theoretically. Here, we analyze an accuracy of spectral clustering, which does not consider overlapping structures, by using the replica method from statistical physics. Our analysis on an overlapping stochastic block model reveals how the structural information is lost from the…
Through discovery of meso-scale structures, community detection methods contribute to the understanding of complex networks. Many community finding methods, however, rely on disjoint clustering techniques, in which node membership is restricted to one community or cluster. This strict requirement limits the ability to inclusively describe communities since some nodes may reasonably be assigned to many communities. We have previously reported Iterative K-core Clustering (IKC), a scalable and modular pipeline that discovers disjoint research communities from the scientific literature. We now pre…
Community detection is an important task in network analysis. A community (also referred to as a cluster) is a set of cohesive vertices that have more connections inside the set than outside. In many social and information networks, these communities naturally overlap. For instance, in a social network, each vertex in a graph corresponds to an individual who usually participates in multiple communities. In this paper, we propose an efficient overlapping community detection algorithm using a seed expansion approach. The key idea of our algorithm is to find good seeds, and then greedily expand t…
Community detection provides invaluable help for various applications, such as marketing and product recommendation. Traditional community detection methods designed for plain networks may not be able to detect communities with homogeneous attributes inside on attributed networks with attribute information. Most of recent attribute community detection methods may fail to capture the requirements of a specific application and not be able to mine the set of required communities for a specific application. In this paper, we aim to detect the set of target communities in the target subspace which …
We propose a new local, deterministic and parameter-free algorithm that detects fuzzy and crisp overlapping communities in a weighted network and simultaneously reveals their hierarchy. Using a local fitness function, the algorithm greedily expands natural communities of seeds until the whole graph is covered. The hierarchy of communities is obtained analytically by calculating resolution levels at which communities grow rather than numerically by testing different resolution levels. This analytic procedure is not only more exact than its numerical alternatives such as LFM and GCE but also muc…
A measure of distance between two clusterings has important applications, including clustering validation and ensemble clustering. Generally, such distance measure provides navigation through the space of possible clusterings. Mostly used in cluster validation, a normalized clustering distance, a.k.a. agreement measure, compares a given clustering result against the ground-truth clustering. Clustering agreement measures are often classified into two families of pair-counting and information theoretic measures, with the widely-used representatives of Adjusted Rand Index (ARI) and Normalized Mut…
Detection of overlapping communities in complex networks has motivated recent research in the relevant fields. Aiming this problem, we propose a Markov dynamics based algorithm, called UEOC, which means, 'unfold and extract overlapping communities'. In UEOC, when identifying each natural community that overlaps, a Markov random walk method combined with a constraint strategy, which is based on the corresponding annealed network (degree conserving random network), is performed to unfold the community. Then, a cutoff criterion with the aid of a local community function, called conductance, which…
Discovering overlapping community structures is a crucial step to understanding the structure and dynamics of many networks. In this paper we develop a symmetric binary matrix factorization model (SBMF) to identify overlapping communities. Our model allows us not only to assign community memberships explicitly to nodes, but also to distinguish outliers from overlapping nodes. In addition, we propose a modified partition density to evaluate the quality of community structures. We use this to determine the most appropriate number of communities. We evaluate our methods using both synthetic bench…
While there has been a plethora of approaches for detecting disjoint communities from real-world complex networks, some methods for detecting overlapping community structures have also been recently proposed. In this work, we argue that, instead of developing separate approaches for detecting overlapping communities, a promising alternative is to infer the overlapping communities from multiple disjoint community structures. We propose an ensemble-based approach, called EnCoD, that leverages the solutions produced by various disjoint community detection algorithms to discover the overlapping co…
Community discovery in the social network is one of the tremendously expanding areas which earn interest among researchers for the past one decade. There are many already existing algorithms. However, new seed-based algorithms establish an emerging drift in this area. The basic idea behind these strategies is to identify exceptional nodes in the given network, called seeds, around which communities can be located. This paper proposes a blended strategy for locating suitable superior seed set by applying various centrality measures and using them to find overlapping communities. The examination…
Agglomerative clustering is a well established strategy for identifying communities in networks. Communities are successively merged into larger communities, coarsening a network of actors into a more manageable network of communities. The order in which merges should occur is not in general clear, necessitating heuristics for selecting pairs of communities to merge. We describe a hierarchical clustering algorithm based on a local optimality property. For each edge in the network, we associate the modularity change for merging the communities it links. For each community vertex, we call the pr…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order structure of a network. Higher-order structures such as the edge embeddedness and the size of communities may play more important roles in many online social networks. In this paper, we provide empirical evidence on the existence of rich higherorder structural characteristics in online social networks, develop mathematical models to interpret and model these …
One of the most remarkable social phenomena is the formation of communities in social networks corresponding to families, friendship circles, work teams, etc. Since people usually belong to several different communities at the same time, the induced overlaps result in an extremely complicated web of the communities themselves. Thus, uncovering the intricate community structure of social networks is a non-trivial task with great potential for practical applications, gaining a notable interest in the recent years. The Clique Percolation Method (CPM) is one of the earliest overlapping community f…
Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping communities. We show that on a wide range of empirical networks, from different domains, significant numbers of cliques are split across the separate partitions produced by these algorithms. We then examine the largest connected component of the subgraph formed by retaining only edges in cliques, and apply partitioning strategies that explicitly minimise the number …
Community discovery in complex networks is an interesting problem with a number of applications, especially in the knowledge extraction task in social and information networks. However, many large networks often lack a particular community organization at a global level. In these cases, traditional graph partitioning algorithms fail to let the latent knowledge embedded in modular structure emerge, because they impose a top-down global view of a network. We propose here a simple local-first approach to community discovery, able to unveil the modular organization of real complex networks. This i…
Although community structure is ubiquitous in complex networks, few works exploit this topological property to control epidemics. In this work, devoted to networks with non-overlapping community structure (i.e, a node belongs to a single community), we propose and investigate three deterministic immunization strategies. In order to characterize the influence of a node, various pieces of information are used such as the number of communities that the node can reach in one hop, the nature of the links (intra community links, inter community links), the size of the communities, and the interconne…
Community detection in networks refers to the process of seeking strongly internally connected groups of nodes which are weakly externally connected. In this work, we introduce and study a community definition based on internal edge density. Beginning with the simple concept that edge density equals number of edges divided by maximal number of edges, we apply this definition to a variety of node and community arrangements to show that our definition yields sensible results. Our community definition is equivalent to that of the Absolute Potts Model community detection method (Phys. Rev. E 81, 0…
Community detection is the process of assigning nodes and links in significant communities (e.g. clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communitie…
Detection of overlapping communities in real-world networks is a generally challenging task. Upon recognizing that a network is in fact the union of its egonets, a novel network representation using multi-way data structures is advocated in this contribution. The introduced sparse tensor-based representation exhibits richer structure compared to its matrix counterpart, and thus enables a more robust approach to community detection. To leverage this structure, a constrained tensor approximation framework is introduced using PARAFAC decomposition. The arising constrained trilinear optimization i…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to characterize the structural organization of hypergraphs. The method allows to infer missing hyperedges of any size in a principled way, and to jointly detect overlapping communities in presence of higher-order interactions. Furthermore, our model has an efficient numerical implementation, and it runs faster than dyadic algorithms on pairwise records project…
Community structure is one of the key properties of real-world complex networks. It plays a crucial role in their behaviors and topology. While an important work has been done on the issue of community detection, very little attention has been devoted to the analysis of the community structure. In this paper, we present an extensive investigation of the overlapping community network deduced from a large-scale co-authorship network. The nodes of the overlapping community network represent the functional communities of the co-authorship network, and the links account for the fact that communitie…
A "community" in a social network is usually understood to be a group of nodes more densely connected with each other than with the rest of the network. This is an important concept in most domains where networks arise: social, technological, biological, etc. For many years algorithms for finding communities implicitly assumed communities are nonoverlapping (leading to use of clustering-based approaches) but there is increasing interest in finding overlapping communities. A barrier to finding communities is that the solution concept is often defined in terms of an NP-complete problem such as C…
We discuss two views on extending existing methods for complex network modeling which we dub the communities first and the networks first view, respectively. Inspired by the networks first view that we attribute to White, Boorman, and Breiger (1976)[1], we formulate the multiple-networks stochastic blockmodel (MNSBM), which seeks to separate the observed network into subnetworks of different types and where the problem of inferring structure in each subnetwork becomes easier. We show how this model is specified in a generative Bayesian framework where parameters can be inferred efficiently usi…
One of the main organizing principles in real-world social, information and technological networks is that of network communities, where sets of nodes organize into densely linked clusters. Even though detection of such communities is of great interest, understanding the structure communities in large networks remains relatively limited. Due to unavailability of labeled ground-truth data it is practically impossible to evaluate and compare different models and notions of communities on a large scale. In this paper we identify 6 large social, collaboration, and information networks where nodes …
Our aim here is to plead for the significance of cultural considerations of overlapping inter-attitudinal patterns right next to well established structural considerations of interorganizational networks based on overlapping membership patterns. In particular, we examine how the analytical sociological methodological incorporation of cultural attributes or attitudes might enhance our understanding of structural community categorizations in interorganizational networks. For this purpose, we analyze data of the International Peace Protest Survey (IPPS) on the world-wide peace protests of Februar…
Complex networks tend to display communities which are groups of nodes cohesively connected among themselves in one group and sparsely connected to the remainder of the network. Detecting such communities is an important computational problem, since it provides an insight into the functionality of networks. Further, investigating community structure in a dynamic network, where the network is subject to change, is even more challenging. This paper presents a game-theoretical technique for detecting community structures in dynamic as well as static complex networks. In our method, each node take…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs capture power law degree distributions (Barabási-Albert) and small-world properties (Watts-Strogatz), but only limited clustering behavior. We introduce a generalization of the classical Erdős-Rényi model of random graphs which provably achieves a wide range of desired clustering coefficient, triangle-to-edge and four-cycle-to-edge ratios for any given graph siz…
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Seeding then expanding is a commonly used scheme to discover overlapping communities in a network. Most seeding methods are either too complex to scale to large networks or too simple to select high-quality seeds, and the non-principled functions used by most expanding methods lead to poor performance when applied to diverse networks. This paper proposes a new method that transforms a network into a corpus where each edge is treated as a document, and all nodes of the network are treated as terms of the corpus. An effective seeding method is also proposed that selects seeds as a training set, …
The detection of overlapping communities is a challenging problem which is gaining increasing interest in recent years because of the natural attitude of individuals, observed in real-world networks, to participate in multiple groups at the same time. This review gives a description of the main proposals in the field. Besides the methods designed for static networks, some new approaches that deal with the detection of overlapping communities in networks that change over time, are described. Methods are classified with respect to the underlying principles guiding them to obtain a network divisi…
