A graph community is a subset of the vertex set of a graph whose vertices share a specified pattern of connectivity. In the common assortative interpretation, a graph community has comparatively many graph edges between its vertices and comparatively few graph edges joining it to the rest of the graph. Other definitions use structural roles or latent classes in a stochastic block model, so there is no single universal criterion for a graph community (Fortunato 2010).
A collection of graph communities may overlap or may form a set partition of the vertex set. Community detection is the problem of finding such communities, whereas graph modularity is one possible score for a proposed partition into communities.
