A small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network.
Small-world properties are found in many real-world phenomena, including road maps, food chains, electric power grids, metabolite processing networks, networks of brain neurons, voter networks, telephone call graphs, and social influence networks.
Networks of connected proteins have small world properties such as power-law obeying degree distributions.[8] Similarly transcriptional networks, in which the nodes are genes, and they are linked if one gene has an up or down-regulatory genetic influence on the other, have small world network properties.[9]

















