Quantifying randomness in real networks

Represented as graphs, real networks are intricate combinations of order= and disorder. Fixing some of the structural properties of network models t= o their values observed in real networks, many other properties appear as s= tatistical consequences of these fixed observables, plus randomness in othe= r respects. Here we employ the dk-series, a complete set of basic character= istics of the network structure, to study the statistical dependencies betw= een different network properties. We consider six real networks-the Interne= t, US airport network, human protein interactions, technosocial web of trus= t, English word network, and an fMRI map of the human brain-and find that m= any important local and global structural properties of these networks are = closely reproduced by dk-random graphs whose degree distributions, degree c= orrelations and clustering are as in the corresponding real network. We dis= cuss important conceptual, methodological, and practical implications of th= is evaluation of network randomness, and release software to generate dk-ra= ndom graphs.