# Generalized communities in networks

A substantial volume of research has been devoted to studies

of community structure in networks,

but communities are not the only possible form of large-scal

e network structure. Here we describe

a broad extension of community structure that encompasses t

raditional communities but includes a

wide range of generalized structural patterns as well. We de

scribe a principled method for detecting

this generalized structure in empirical network data and de

monstrate with real-world examples how

it can be used to learn new things about the shape and meaning o

f networks.

The detection and analysis of large-scale structure in

networks has been the subject of a vigorous research

effort in recent years, in part because of the highly

successful application of ideas drawn from statistical

physics [1, 2]. Particular energy has been devoted to

the study of community structure, meaning the division

of networks into densely connected subgroups, a common

and revealing feature, especially in social and biological

networks [3]. Community structure is, however, only one

of many possibilities where real-world networks are con-

cerned. In this paper, we describe a broad generaliza-

tion of community structure that encompasses not only

traditional communities but also overlapping or fuzzy

communities, ranking or stratified structure, geometric

networks, and a range of other structural types, yet is

easily and flexibly detected using a fast, mathematically

principled procedure which we describe. We give demon-

strative applications of our approach to both computer-

generated test networks and real-world examples.

Community structure can be thought of as a division

of the nodes of a network into disjoint groups such that

the probability of an edge is higher between nodes in

the same group than between nodes in different groups.

For instance, one can generate artificial networks with

community structure using the stochastic block model, a

mathematical model that follows exactly this principle.

In the stochastic block model the nodes of a network...