The Emergence of Informative Higher Scales in Complex Networks

Figure 1

Effective information depends on network structure. (a) In Erdős-Rényi (ER) networks, we see the network’s level off at as , the network’s size, increases (log scale shown). (b) The of networks grown under a preferential attachment mechanism, which depends on the preferential attachment exponent, . Under this network growth model, new nodes add their edges (here, ) to existing nodes in the network with a probability proportional to . Only sublinear preferential attachment allows for the continuous growth of with the growth of the network. The ribbons around the data represent standard deviations after 100 simulations of each.

(a)

(b)