Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-05-10
Phys. Rev. E 82, 066118 (2010)
Physics
Condensed Matter
Statistical Mechanics
12 pages, 6 figures, 1 table
Scientific paper
10.1103/PhysRevE.82.066118
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly non-tree-like neighborhoods that contain short loops, cliques, or other biconnected subgraphs. In this paper we propose and analyze a new class of random graph models that incorporates general subgraphs, allowing for non-tree-like neighborhoods while still remaining solvable for many fundamental network properties. Among other things we give solutions for the size of the giant component, the position of the phase transition at which the giant component appears, and percolation properties for both site and bond percolation on networks generated by the model.
Karrer Brian
Newman M. E. J.
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