Many real-world networks have been evolving, and are finely modeled as temporal graphs from the viewpoint of the graph theory. A temporal graph is informative, and always contains two types of information, i.e., the temporal information and topological information, where the temporal information reflects the time when the relationships are established, and the topological information focuses on the structure of the graph. In this paper, we perform time-topology analysis on temporal graphs to extract useful information. Firstly, a new metric named T-cohesiveness is proposed to evaluate the cohesiveness of a temporal subgraph. It defines the cohesiveness of a temporal subgraph from the time and topology dimensions jointly. Specifically, given a temporal graph
G
s
= (
Vs
, ε
Es
), cohesiveness in the time dimension reflects whether the connections in
G
s
happen in a short period of time, while cohesiveness in the topology dimension indicates whether the vertices in
V
s
are densely connected and have few connections with vertices out of
G
s
. Then, T-cohesiveness is utilized to perform time-topology analysis on temporal graphs, and two time-topology analysis methods are proposed. In detail, T-cohesiveness evolution tracking traces the evolution of the T-cohesiveness of a subgraph, and combo searching finds out all the subgraphs that contain the query vertex and have T-cohesiveness larger than a given threshold. Moreover, a pruning strategy is proposed to improve the efficiency of combo searching. Experimental results confirm the efficiency of the proposed time-topology analysis methods and the pruning strategy.
Efficient distributed reachability querying of massive temporal graphs
