Representation, simulation, and visualization of financial networks

Networks can be represented by a list of pairs, by an adjacency matrix, or by graphs. Graphs consist of vertices and edges (nodes). In R, vertices are numbered and may have several attributes. Between two vertices there can exist an edge (directed or undirected, weighted or non-weighted), and the edge may have other attributes as well. In most financial networks, vertices stand for market players, while edges describe different sorts of financial linkages between them.

Using the built-in R tools and some function from the igraph package, it is easy to create/simulate artificial networks. The following table (Table 1) summarizes some important network types and their basic properties:

Network	Clustering	Average path length	Degree distribution
Regular (for example, ring, full)	High	High	Equal or fixed in-out degrees in each node
Pure random (for example, Erdős-Rényi)	Low	Low	Exponential, Gaussian
Scale free	Variable...