  Community search, retrieving the cohesive subgraph which contains the query
vertex, has been widely touched over the past decades. The existing studies on
community search mainly focus on static networks. However, real-world networks
usually are temporal networks where each edge is associated with timestamps.
The previous methods do not work when handling temporal networks. We study the
problem of identifying the significant engagement community to which the
user-specified query belongs. Specifically, given an integer k and a query
vertex u, then we search for the subgraph H which satisfies (i) u $\in$ H; (ii)
the de-temporal graph of H is a connected k-core; (iii) In H that u has the
maximum engagement level. To address our problem, we first develop a top-down
greedy peeling algorithm named TDGP, which iteratively removes the vertices
with the maximum temporal degree. To boost the efficiency, we then design a
bottom-up local search algorithm named BULS and its enhanced versions BULS+ and
BULS*. Lastly, we empirically show the superiority of our proposed solutions on
six real-world temporal graphs.
