  This article presents an efficient hierarchical clustering algorithm that
solves the problem of core community detection. It is a variant of the standard
community detection problem in which we are particularly interested in the
connected core of communities. To provide a solution to this problem, we
question standard definitions on communities and provide alternatives. We also
propose a function called compactness, designed to assess the quality of a
solution to this problem. Our algorithm is based on a graph traversal
algorithm, the LexDFS. The time complexity of our method is in $O(n\times
log(n))$. Experiments show that our algorithm creates highly compact clusters.
