  Community search that finds query-dependent communities has been studied on
various kinds of graphs. As one instance of community search, intimate-core
group search over a weighted graph is to find a connected $k$-core containing
all query nodes with the smallest group weight. However, existing
state-of-the-art methods start from the maximal $k$-core to refine an answer,
which is practically inefficient for large networks. In this paper, we develop
an efficient framework, called local exploration k-core search (LEKS), to find
intimate-core groups in graphs. We propose a small-weighted spanning tree to
connect query nodes, and then expand the tree level by level to a connected
$k$-core, which is finally refined as an intimate-core group. We also design a
protection mechanism for critical nodes to avoid the collapsed $k$-core.
Extensive experiments on real-life networks validate the effectiveness and
efficiency of our methods.
