Graphs with complex stochastic increments

A new class of graphs is introduced in preferential attachment random graphs theory, these graphs are grown by adding an infinite number of complex stochastic increments, consisting of several interconnected vertices. The problems of final degree distributions for vertices and edges of growing graphs are solved by analytic methods. Analytic solution of a graph calibration (synthesis) problem due to the given final degrees distribution of vertices and edges is derived. Numerical method is developed for a complex graph calibration by vertex degree distributions together with edge degrees and clustering coefficient. The examples of the complex graph calibration in real network modeling are given.