  Community search is a problem aimed at searching for densely connected
subgraphs within a network based on query conditions, which has recently
attracted significant attention. However, most previous community search
studies have overlooked the coexistence relationship among attributes. They
typically assign a single attribute to each node or edge (e.g.,only considering
influence scores or keywords), which is difficult for users to obtain a
comprehensive and beneficial information. Additionally, most of them also
ignored the uncertainty in the attribute graph. Therefore, in this paper, we
introduce two novel community models, namely topic-based interaction graph and
$(k,l,\eta)$-influential community. The former is a directed ucertain graph
generated by the query topic distribution provided by users, while the latter
is used for solving the topic-aware most influential community search problem
in social networks. Furthermore, we propose an online search algorithm which
computes the influence value of each vertex by considering the topic-aware
information diffusion process on interaction graphs. And then, we use a
peeling-pruning strategy to iteratively find the topic-aware most
$(k,l,\eta)$-influential community. To further speed up the search performance,
we devise two lightweight index structures which efficiently support the search
for the topic-aware most influential community within an optimal time. We also
propose three optimization methods to improve the space and time costs of the
index-based approach.
