Networks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community structure in single (i.e., monoplex) networks. However, with the advent of relational data with multiple modalities, multiplex networks, i.e., networks composed of multiple layers representing different aspects of relations, have emerged. Consequently, community detection in multiplex network, i.e., detecting clusters of nodes shared by all layers, has become a new challenge. In this paper, we propose Network Fusion for Composite Community Extraction (NF-CCE), a new class of algorithms, based on four different non-negative matrix factorization models, capable of extracting composite communities in multiplex networks. Each algorithm works in two steps: first, it finds a non-negative, low-dimensional feature representation of each network layer; then, it fuses the feature representation of layers into a common non-negative, low-dimensional feature representation via collective factorization. The composite clusters are extracted from the common feature representation. We demonstrate the superior performance of our algorithms over the state-of-the-art methods on various types of multiplex networks, including biological, social, economic, citation, phone communication, and brain multiplex networks.
Although, there is no universally accepted mathematical definition of the community notion in graphs, the probably most commonly accepted definition is the following: a community is a set of nodes in a network that are connected more densely among each other than they are to the rest of the network @cite_0 . Hence, the problem of community detection is as follows: given an adjacency matrix @math of one network with @math nodes and @math communities, find the community assignment of all nodes, denoted by @math , where @math if nodes @math belongs to community @math , and @math otherwise. We consider the case of non-overlapping communities, where a node can belong to only one community, i.e., @math .
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Community detection is a common problem in graph data analytics that consists of finding groups of densely connected nodes with few connections to nodes outside of the group. In particular, identifying communities in large-scale networks is an important task in many scientific domains. In this review, we evaluated eight state-of-the-art and five traditional algorithms for overlapping and disjoint community detection on large-scale real-world networks with known ground-truth communities. These 13 algorithms were empirically compared using goodness metrics that measure the structural properties of the identified communities, as well as performance metrics that evaluate these communities against the ground-truth. Our results show that these two types of metrics are not equivalent. That is, an algorithm may perform well in terms of goodness metrics, but poorly in terms of performance metrics, or vice versa. © 2014 The Authors. WIREs Computational Community detection in graphs is the problem of finding groups of vertices which are more densely connected than they are to the rest of the graph. This problem has a long history, but it is currently motivated by social and biological networks. While there are many ways to formalize it, one of the most popular is as an inference problem, where there is a planted “ground truth” community structure around which the graph is generated probabilistically. Our task is then to recover the ground truth knowing only the graph. Recently it was discovered, first h euristically i n p hysics a nd then rigorously in probability and computer science, that this problem has a phase transition at which it suddenly becomes impossible. Namely, if the graph is too sparse, or the probabilistic process that generates it is too noisy, then no algorithm can find a partition t hat i s correlated with the planted one—or even tell if there are communities, i.e., distinguish the graph from a purely random one with high probability. Above this information-theoretic threshold, there is a second threshold beyond which polynomial-time algorithms are known to succeed; in between, there is a regime in which community detection is possible, but conjectured to be exponentially hard. For computer scientists, this field offers a wealth of new ideas and open questions, with connections to probability and combinatorics, message-passing algorithms, and random matrix theory. Perhaps more importantly, it provides a window into the cultures of statistical physics and statistical inference, and how those cultures think about distributions of instances, landscapes of solutions, and hardness. Abstract Community detection in networks is one of the most popular topics of modern network science. Communities, or clusters, are usually groups of vertices having higher probability of being connected to each other than to members of other groups, though other patterns are possible. Identifying communities is an ill-defined problem. There are no universal protocols on the fundamental ingredients, like the definition of community itself, nor on other crucial issues, like the validation of algorithms and the comparison of their performances. This has generated a number of confusions and misconceptions, which undermine the progress in the field. We offer a guided tour through the main aspects of the problem. We also point out strengths and weaknesses of popular methods, and give directions to their use. 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 these seeds based on a community metric. Within this seed expansion method, we investigate the problem of how to determine good seed nodes in a graph. In particular, we develop new seeding strategies for a personalized PageRank clustering scheme that optimizes the conductance community score. An important step in our method is the neighborhood inflation step where seeds are modified to represent their entire vertex neighborhood. Experimental results show that our seed expansion algorithm outperforms other state-of-the-art overlapping community detection methods in terms of producing cohesive clusters and identifying ground-truth communities. We also show that our new seeding strategies are better than existing strategies, and are thus effective in finding good overlapping communities in real-world networks.