Structure of Heterogeneous Networks

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.

💡 Research Summary

The paper addresses a fundamental shortcoming in the analysis of heterogeneous networks—systems that contain multiple types of entities (e.g., people, events, papers, products) and multiple types of links connecting them. Traditional network‑analysis pipelines typically collapse such data into a single‑type graph, either by projecting bipartite relations onto one side or by ignoring cross‑type edges altogether. This projection inevitably conflates distinct relational semantics and discards valuable structural information, limiting the ability to uncover nuanced community structures or to identify truly influential nodes.

To overcome this limitation the authors propose a rigorous mathematical framework that keeps the full multi‑type nature of the data intact. They formalize a heterogeneous network as a set of entity types (V^{(t)}) (t = 1,…,T) and a set of link types (E^{(k)}) (k = 1,…,K). Each pair of entity types ((t, s)) is associated with a block adjacency matrix (A^{(ts)}) that records the connections between nodes of type (t) and nodes of type (s). Stacking all blocks yields a large block‑matrix (M) that fully represents the network without any projection.

The core methodological contribution is a generalization of Bonacich centrality to this block‑matrix setting. Classical Bonacich centrality is defined for a single‑type graph as \