Abstract
In this work we give a community detection algorithm in which the communities both respects the intrinsic order of a directed acyclic graph and also finds similar nodes. We take inspiration from classic similarity measures of bibliometrics, used to assess how similar two publications are, based on their relative citation patterns. We study the algorithm’s performance and antichain properties in artificial models and in real networks, such as citation graphs and food webs. We show how well this partitioning algorithm distinguishes and groups together nodes of the same origin (in a citation network, the origin is a topic or a research field). We make the comparison between our partitioning algorithm and standard hierarchical layering tools as well as community detection methods. We show that our algorithm produces different communities from standard layering algorithms.
Highlights
Nodes in networks have many natural orders
Our focus has been on Directed Acyclic Graphs (DAGs) where the implicit order in such networks prohibits the direct connection of many similar nodes
As this order is intrinsic to the very nature of a DAG, our response has been to embrace this order as it reflects important features of the data
Summary
Nodes in networks have many natural orders. Every centrality measure allows us to say if one node has a higher centrality value than another. Some systems can have important constraint leading to a characteristic order in a network; examples include the publication dates of papers in a citation network, dependency of packages in computer software, and predator-prey relationships in a food web. If edges respect this order, they exist only if they link a high value node to a lower value node, from an earlier paper to a later paper, edges are directed and there can be no cycles — a Directed Acyclic Graph (DAG). The last of these three papers cites the two earlier publications but there is no citation between the first two
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