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The Erdos-Renyi classical random graph is characterized by a fixed linkingprobability for all pairs of vertices. Here, this concept is generalized bydrawing the linking probability from a certain distribution. Such a procedureis found to lead to a static complex network with an arbitrary connectivitydistribution. In particular, a scale-free network with the hierarchicalorganization is constructed without assuming any knowledge about the globallinking structure, in contrast to the preferential attachment rule for agrowing network. The hierarchical and mixing properties of the staticscale-free network thus constructed are studied. The present approachestablishes a bridge between a scalar characterization of individual verticesand topology of an emerging complex network. The result may offer a clue forunderstanding the origin of a few abundance of connectivity distributions in awide variety of static real-world networks.Comment: 15 pages and 3 figure

HIERARCHICAL AND MIXING PROPERTIES OF STATIC COMPLEX NETWORKS EMERGING FROM FLUCTUATING CLASSICAL RANDOM GRAPHS