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
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A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases. Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest neighbors, and which are indicated by the presence of motifs. We show how motifs can be used to define general classes of nodes, including communities, by extending the mathematical expression of Newman?Girvan modularity. We construct then a general framework and apply it to some synthetic and real networks.