Community detection in directed acyclic graphs of adversary interactions

Certain real networks are represented as directed acyclic graphs (DAGs) and the links represent adversary interactions between two entities, such as food webs where links exist only from prey to predators and temporal war networks where links point from attackers to defenders. In such DAGs, similar nodes may form communities, such as top carnivores in food webs and war alliances in war networks, where nodes cannot be directly connected but have similar orders and neighbors. However, most previous community detection methods are developed based on an assumption that a link between nodes indicates similarity, not applicable to such cases. In this work, we define the community in DAGs of adversary interactions based on the nodes' orders and similarities, and propose a Katz-Simrank method to detect communities. We first convert the DAG into an equivalent weighted undirected network based on nodes' orders and similarities, then the problem of community detection in such DAG can be converted into an equivalent problem of detecting cliques in this weighted undirected network. We apply this method to both synthetic and real DAGs, such as food webs and war networks, and find that Katz-Simrank method could effectively identify communities and demonstrates superior performance over other baseline methods in DAG community detection.