Fractal Fingerprint for Network Topologies

We show that the bitmap of sorted adjacency matrix (BOSAM) as a network visualisation tool is able to illustrate a number of network topological properties. It can be used to compare between networks, validate network models and discover new structures in networks. A network’s BOSAM consists of a series of petal-like sections, each of which is outlined by an envelope. We prove and demonstrate that for a given network, the BOSAM envelopes have a fractal relation, which allows us to use one envelope to predict all other envelopes. Also the BOSAM envelopes scale with the size of a network if the network preserves its topology during growth. We analogise a network’s BOSAM envelope to human’s fingerprint as they share a number of common properties, e.g. they are in a simple form, easy to obtain and store, valid for life, strongly characteristic, and encoding essential information for identification.