Mining Diversified Top-$r$r Lasting Cohesive Subgraphs on Temporal Networks

Temporal subgraph mining is recently ubiquitous. Identifying diversified and lasting ingredients is a fundamental problem in analyzing temporal networks. In this paper, we investigate the problem of finding diversified lasting cohesive subgraphs from temporal networks. Specifically, we first introduce a new model, called maximal lasting
$(k,\sigma)$
-core, for characterizing lasting cohesive subgraphs on temporal networks so as to the nodes in the subgraph are connected densely and also the subgraph's structure remains unchanged for a period of time. To enhance the diversity of results, we then formulate a diversified lasting cohesive subgraphs problem, which finds
$r$
maximal lasting
$(k,\sigma)$
-cores with maximum coverage regarding the number of vertices and timestamps. Unfortunately, we show that the optimization problem is NP-hard. To tackle this issue, we first devise a greedy algorithm named
GreLC
with (1-1/e) approximation ratio. However,
GreLC
has prohibitively high time and space complexity, resulting in poor scalability. Then, an improved DFS-based search algorithm called
TopLC
with 1/4 approximation ratio is proposed to lower the computational cost. Finally, empirical studies on six real-world temporal networks demonstrate that the proposed solutions perform efficiently and accurately, and our model is better than temporal cohesive subgraphs detected by existing approaches.