Analyzing Temporal Influence of Burst Vertices in Growing Social Simplicial Complexes

Simplicial complexes provide a useful framework of higher-order networks that model co-occurrences and interactions among more than two elements, and are also equipped with a mathematical foundation in algebraic topology. In this paper, we investigate the temporal growth processes of simplicial complexes derived from human activities and communication on social media from a perspective of burst vertices. First, we empirically show that most of new simplices contain burst vertices, while for each new simplex containing a burst vertex, its vertices other than the corresponding burst vertex do not necessarily co-occur with the burst vertex itself within the not so distant past. We thus examine the problem of finding which burst vertex is contained in a new simplex from the occurrence history of burst vertices. In particular, we focus on analyzing the influence of the occurrence events of burst vertices in terms of time-decays. To this end, we propose a probabilistic model incorporating a log-normal-like time-decay factor and give its learning method. Using real social media datasets, we demonstrate the significance of the proposed model in terms of prediction performance, and uncover the time-decay effects of burst vertices in the occurrence of new simplices by applying the proposed model.