Mining Stable Quasi-Cliques on Temporal Networks

Real-world networks, such as phone-call networks and social networks, are often not static but temporal. Mining cohesive subgraphs from static graphs is a fundamental task in network analysis and has been widely investigated in the past decades. However, the concepts of cohesive subgraphs shift from static to temporal graphs raise many important problems. For instance, how to detect stable cohesive subgraphs on temporal networks such that the nodes in the subgraph are densely and stably connected over time. To address this problem, we resort to the conventional quasi-clique and propose a new model, called maximal
$\rho $
-stable (
$\delta, \gamma $
)-quasi-clique, to capture both the cohesiveness and the stability of a subgraph. We show that the problem of enumerating all maximal
$\rho $
-stable (
$\delta, \gamma $
)-quasi-cliques is NP-hard. To efficiently tackle our problem, we first devise a novel temporal graph reduction algorithm to significantly reduce the temporal graph without losing any maximal
$\rho $
-stable (
$\delta, \gamma $
)-quasi-clique. Then, on the reduced temporal graph, we propose an effective branch and bound enumeration algorithm, named
BB&SCM
, with four carefully designed pruning techniques to accomplish the enumeration process. Finally, we conduct extensive experiments on seven real-world temporal graphs, and the results demonstrate that the temporal graph reduction algorithm can safely reduce 98% nodes of the temporal graph (with millions of nodes and edges) and
BB&SCM
is at least two orders of magnitude faster than the baseline algorithms. Moreover, we also evaluate the effectiveness of our model against other baseline models.