Generalized preferential attachment: tunable power-law degree\n distribution and clustering coefficient

We propose a wide class of preferential attachment models of random graphs,\ngeneralizing previous approaches. Graphs described by these models obey the\npower-law degree distribution, with the exponent that can be controlled in the\nmodels. Moreover, clustering coefficient of these graphs can also be\ncontrolled. We propose a concrete flexible model from our class and provide an\nefficient algorithm for generating graphs in this model. All our theoretical\nresults are demonstrated in practice on examples of graphs obtained using this\nalgorithm. Moreover, observations of generated graphs lead to future questions\nand hypotheses not yet justified by theory.\n