See Measures and metrics for networks

Many networks naturally divide into groups. These are substructures that are prominent for some reason. Simple examples are:

• clique: a maximal subset of the vertices in an undirected network such that every member of the set is connected by an edge to every other.
• Generalizing the above, a k-plex of size $n$ is a maximal subset of $n$ vertices within a network such that each vertex is connected to at least $n-k$ of the others. We could define this using fractions of others as well.
• A k-core is a maximal (i.e. it is not a subset of a k-core) subset of vertices such that each is connected to at least $k$ others in the subset. A way to find them is to successively remove vertices with degree less than $k$.
• k-clique: a maximal subset of vertices such that each is no more than a distance $k$ away from any of the others via the edges of the network. See also k-club and k-clanl

Many other definitions related to the idea of "groups"

Generalization of components: k-component is a maximal subset of nodes such that each is reachable from each of the other by at least $k$ vertex-independent paths. Equivalently no vertices in this set can be disconnected by removing less than $k$ vertices see cut sets. A variant can be defined using edge-independent paths.