The Emergence of Informative Higher Scales in Complex Networks
Comparing determinism and degeneracy. (a) Left column: three example out-weight vectors, , of a given node, . A maximally deterministic vector (top left, where the corresponds to node in the inset network motif) is when a random walker on transitions to one of its neighbors with probability 1.0, whereas indeterminism occurs when has a uniform probability of visiting any node in the network in the next time step. Right: three example in-weight vectors to a given . A maximally degenerate vector, (top right, exemplified by the inset network motif), is when every outgoing edge in the network connects to a single node, whereas minimal degeneracy occurs when each value in is uniformly . (b) By comparing the determinism and degeneracy of canonical network structures, we find a great deal of heterogeneity in different network models’ ratios between their determinism and degeneracy. High degeneracy is characterized by hub-and-spoke topology, as in the case of the star network. Networks with high determinism are characterized by longer average path lengths, as in the case of a ring lattice.
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