  Clusters or communities can provide a coarse-grained description of complex
systems at multiple scales, but their detection remains challenging in
practice. Community detection methods often define communities as dense
subgraphs, or subgraphs with few connections in-between, via concepts such as
the cut, conductance, or modularity. Here we consider another perspective built
on the notion of local dominance, where low-degree nodes are assigned to the
basin of influence of high-degree nodes, and design an efficient algorithm
based on local information. Local dominance gives rises to community centers,
and uncovers local hierarchies in the network. Community centers have a larger
degree than their neighbors and are sufficiently distant from other centers.
The strength of our framework is demonstrated on synthesized and empirical
networks with ground-truth community labels. The notion of local dominance and
the associated asymmetric relations between nodes are not restricted to
community detection, and can be utilised in clustering problems, as we
illustrate on networks derived from vector data.
