Network community profile plot characterizes the best possible community over a range of size scales. We use a natural and widely-adopted notion of community goodness called conductance, also known as the normalized cut metric. Conductance can be thought of as the number of edges pointing outside the community divided by the number of edges inside the community.
In contrast to small networks that often exhibit unambiguous community structure, large networks have a nested core-periphery structure, consisting of a large moderately well-connected core and a large number of small very well-connected communities barely connected to the core. Network communities tend to exist only at small size scales of up to about 100 nodes, while at larger size scales network communities become less community-like.
Network datasets can be downloaded at: http://snap.stanford.edu/data.
Code for computing NCP plots can be downloaded at: http://snap.stanford.edu/snap.
Unzip the code and refer to examples/ncpplot for the application.
NCP plot of the friendship network of the LiveJournal
online social network: