  Many networks in real-life typically contain parts in which some nodes are
more highly connected to each other than the other nodes of the network. The
collection of such nodes are usually called clusters, communities, cohesive
groups or modules. In graph terminology, it is called highly connected graph.
In this paper, we first prove some properties related to highly connected
graph. Based on these properties, we then redefine the highly connected
subgraph which results in an algorithm that determines whether a given graph is
highly connected in linear time. Then we present a computationally efficient
algorithm, called MOHCS, for mining overlapping highly connected subgraphs. We
have evaluated experimentally the performance of MOHCS using real and synthetic
data sets from computer-generated graph and yeast protein network. Our results
show that MOHCS is effective and reliable in finding overlapping highly
connected subgraphs. Keywords-component; Highly connected subgraph, clustering
algorithms, minimum cut, minimum degree
