Dense Subgraph Discovery Meets Strong Triadic Closure

Finding dense subgraphs is a core problem with numerous graph mining applications such as community detection in social networks and anomaly detection. However, in many real-world networks connections are not equal. One way to label edges as either strong or weak is to use strong triadic closure (STC). Here, if one node connects strongly with two other nodes, then those two nodes should be connected at least with a weak edge. STC-labelings are not unique and finding the maximum number of strong edges is NP-hard. In this paper, we apply STC to dense subgraph discovery. More formally, our score for a given subgraph is the ratio between the sum of the number of strong edges and weak edges, weighted by a user parameter λ, and the number of nodes of the subgraph. Our goal is to find a subgraph and an STC-labeling maximizing the score. We show that for λ = 1, our problem is equivalent to finding the densest subgraph, while for λ = 0, our problem is equivalent to finding the largest clique, making our problem NP-hard. We propose an exact algorithm based on integer linear programming and four practical polynomial-time heuristics. We present an extensive experimental study that shows that our algorithms can find the ground truth in synthetic datasets and run efficiently in real-world datasets.