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Metric structure of random networks
S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and…
How to generate a random growing network
S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin
We propose a construction procedure which generates a wide class of random evolving networks with fat-tailed degree distributions and an arbitrary clustering. This procedure applie…
How to construct a correlated net
S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin
(a) We propose a ``static'' construction procedure for random networks with given correlations of the degrees of the nearest-neighbor vertices. This is an equilibrium graph, maxima…
Ising Model on Networks with an Arbitrary Distribution of Connections
S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes
We find the exact critical temperature of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution . We obs…
Accelerated growth of networks
S. N. Dorogovtsev, J. F. F. Mendes
In many real growing networks the mean number of connections per vertex increases with time. The Internet, the Word Wide Web, collaboration networks, and many others display this b…
Principles of statistical mechanics of random networks
S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partiti…