4. Descriptive Analysis of Network Graph Characteristics

In the study of a given complex system, questions of interest can often be re-phrased in a useful manner as questions regarding some aspect of the structure or characteristics of a corresponding network graph. For example, various types of basic social dynamics can be represented by triplets of vertices with a particular pattern of ties among them (i.e., triads); questions involving the movement of information or commodities usually can be posed in terms of paths on the network graph and flows along those paths; certain notions of the ‘importance’ of individual system elements may be captured by measures of how ‘central’ the corresponding vertex is in the network; and the search for ‘communities’ and analogous types of unspecified ‘groups’ within a system frequently may be addressed as a graph partitioning problem.