Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually project such networks unto simple graphs composed of entities of a single type. In the process, they conflate relations between entities of different types and loose important structural information.We develop a mathematical framework that can be used to compactly represent and analyze heterogeneous networks that combine multiple entity and link types.We generalize Bonacich centrality, which measures connectivity between nodes by the number of paths between them, to heterogeneous networks and use this measure to study network structure. Specifically, we extend the popular modularity-maximization method for community detection to use this centrality metric. We also rank nodes based on their connectivity to other nodes. One advantage of this centrality metric is that it has a tunable parameter we can use to set the length scale of interactions. By studying how rankings change with this parameter allows us to identify important nodes in the network.We apply the proposed method to analyze the structure of several heterogeneous networks. We show that exploiting additional sources of evidence corresponding to links between, as well as among, different entity types yields new insights into network structure.
There has been some work in motif-based communities in complex networks @cite_17 which like our work extends traditional notion of modularity introduced by Girvan and Newman @cite_20 . The underlying motivation for motif-based community detection is that the high density of edges within a community determines correlations between nodes going beyond nearest-neighbours,'' which is also our motivation for applying centrality-based modularity to community detection. Though the motivation of this method is to determine the correlations between nodes beyond nearest neighbors, yet it does impose a limit on the proximity of neighbors to be taken into consideration dependent on the size of the motifs. The method we propose, on the other hand, imposes no such limit on proximity. On the contrary, it considers the correlation between nodes in a more global sense. The measure of global correlation evaluated using the b-centrality metric would be equal to the weighted average of correlations when motifs of different sizes are taken. B-centrality enables us to calculate this complex term quickly and efficiently.
@cite_20 @cite_17
2015953751 1976160665 144379121 2152091390
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks. Graph clustering has been widely applied in exploring regularities emerging in relational data. Recently, the rapid development of network theory correlates graph clustering with the detection of community structure, a common and important topological characteristic of networks. Most existing methods investigate the community structure at a single topological scale. However, as shown by empirical studies, the community structure of real world networks often exhibits multiple topological descriptions, corresponding to the clustering at different resolutions. Furthermore, the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree. It is very challenging to detect multiscale community structure in heterogeneous networks. In this paper, we propose a novel, unified framework for detecting community structure from the perspective of dimensionality reduction. Based on the framework, we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction. We then propose a novel method to detect communities at multiple topological scales within our framework. We further show that existing algorithms fail to deal with heterogeneous node degrees. We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework. Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks. In this paper we present an original approach for community detection in complex networks. The approach belongs to the family of seed-centric algorithms. However, instead of expanding communities around selected seeds as most of existing approaches do, we explore here applying an ensemble clustering approach to different network partitions derived from ego-centered communities computed for each selected seed. Ego-centered communities are themselves computed applying a recently proposed ensemble ranking based approach that allow to efficiently combine various local modularities used to guide a greedy optimization process. Results of first experiments on real world networks for which a ground truth decomposition into communities are known, argue for the validity of our approach. Measuring the centrality of nodes in real-world networks has remained an important task in the technological, social, and biological network paradigms carrying implications on their analysis and applications. Exact inference of centrality values is infeasible in large networks due to the need to solve the all-pairs shortest path problem. We introduce a framework to approximate node centralities in real-world networks that are known to exhibit modularity, i.e., the presence of dense subgraphs or communities, which are themselves sparsely connected. We also propose a novel centrality measure known as Community Inbetweenness that ranks nodes based solely on community information. In a modular network of size n with √n(1 2) evenly sized communities and m edges, our framework requires linear time O(m) and O(√nm) time for the approximation of closeness and betweenness respectively. Utilizing a recently proposed linear time method in community detection, our approximation techniques are faster than traditional sampling algorithms, applicable in real-time distributed environments, and offer highly comparable results.