The standard mathematical approach to describe Networks is that of Graphs. A Graph is composed by a set of vertices and a set of connection between them. Those connections are called edges.

Among the various quantities describing the properties of these sets, the most immediate is the degree that is the number of edges per vertex. Another quantity that is important is the distance between two vertices. Distance is defined as the minimum number of edges one has to travel to pass from one vertex to another.

In almost any real network one can verify that degree is power law distributed and distance is usually peaked on very small values. The first phenomenon is known as scale invariance the second is known as small world effect.

-- GuidoCaldarelli - 05 Nov 2005