  Usually the boundary of a community in a network is drawn between nodes and
thus crosses its outgoing links. If we construct overlapping communities by
applying the link-clustering approach nodes and links interchange their roles.
Therefore, boundaries must drawn through the nodes shared by two or more
communities. For the purpose of community evaluation we define a conductance of
boundary nodes of overlapping communities analogously to the graph conductance
of boundary-crossing links used to partition a graph into disjoint communities.
We show that conductance of boundary nodes (or normalised node cut) can be
deduced from ordinary graph conductance of disjoint clusters in the network's
weighted line graph introduced by Evans and Lambiotte (2009) to get overlapping
communities of nodes in the original network. We test whether our definition
can be used to construct meaningful overlapping communities with a local greedy
algorithm of link clustering. In this note we present encouraging results we
obtained for Zachary's karate-club network.
