Subgroups, or sub-communities, within a network are groups of nodes which are particularly close to each other as compared to other nodes in the network. Subgroup properties are different from nodal and structural network statistics because they involve no less than three nodes, but do not involve all nodes in a network. Additionally, they are used to determine the presence of a subgroup, in which all nodes have similar properties. Common subgroup properties include complete mutuality, diameter, degree, and differential degree.

Complete mutuality (cliques)

The most rigorous of subgroup properties, this property requires that all nodes in a subgroup are connected to all other nodes. Subgroups with complete mutuality are commonly referred to as cliques.

Reachability and diameter (n-cliques)

Subgroups which do not have complete mutuality, but all nodes are within a distance of n from each other are commonly referred to as n-cliques. The smaller n, the more strict this property becomes, with n=1 yielding a completely connected subgroup, or clique.

Degree (k-plexes)

Subgroups based upon nodal degree require high degree for each node in the subgroup, such that members of the subgroup have high connectivity with other members. A subgroup of size g_s is known as a k-plex if it has no fewer than (g_s – k) connections.

Differential Degree (LS Sets)

The property of differential degree requires that a subgroup not have a high number of connections in absolute terms, but that it have a high number of connections within itself relative to the number of connections that it has to nodes that are not a part of that subgroup. An LS Set is a subgroup which has more internal connections than it does connections to nodes outside the subgroup.