  A great variety of complex systems ranging from user interactions in
communication networks to transactions in financial markets can be modeled as
temporal graphs, which consist of a set of vertices and a series of timestamped
and directed edges. Temporal motifs in temporal graphs are generalized from
subgraph patterns in static graphs which take into account edge orderings and
durations in addition to structures. Counting the number of occurrences of
temporal motifs is a fundamental problem for temporal network analysis.
However, existing methods either cannot support temporal motifs or suffer from
performance issues. In this paper, we focus on approximate temporal motif
counting via random sampling. We first propose a generic edge sampling (ES)
algorithm for estimating the number of instances of any temporal motif.
Furthermore, we devise an improved EWS algorithm that hybridizes edge sampling
with wedge sampling for counting temporal motifs with 3 vertices and 3 edges.
We provide comprehensive analyses of the theoretical bounds and complexities of
our proposed algorithms. Finally, we conduct extensive experiments on several
real-world datasets, and the results show that our ES and EWS algorithms have
higher efficiency, better accuracy, and greater scalability than the
state-of-the-art sampling method for temporal motif counting.
