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93 lines
2.5 KiB
93 lines
2.5 KiB
dms(1) -- Grow a scale-free random graph with tunable exponent
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======
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## SYNOPSIS
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`dms` <N> <m> <n0> _a_
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## DESCRIPTION
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`dms` grows an undirected random scale-free graph with <N> nodes using
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the modified linear preferential attachment model proposed by
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Dorogovtsev, Mendes and Samukhin. The initial network is a clique of
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<n0> nodes, and each new node creates <m> new edges. The resulting
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graph will have a scale-free degree distribution, whose exponent
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converges to `gamma=3.0 + a/m` for large <N>.
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## PARAMETERS
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* <N>:
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Number of nodes of the final graph.
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* <m>:
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Number of edges created by each new node.
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* <n0>:
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Number of nodes in the initial (seed) graph.
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* _a_:
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This parameter sets the exponent of the degree distribution
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(`gamma = 3.0 + a/m`). _a_ must be larger than <-m>.
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## OUTPUT
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`dms` prints on STDOUT the edge list of the final graph.
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## EXAMPLES
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Let us assume that we want to create a scale-free network with
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<N=10000> nodes, with average degree equal to 8, whose degree
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distribution has exponent
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gamma = 2.5
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Since `dms` produces graphs with scale-free degree sequences with an
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exponent `gamma = 3.0 + a/m`, the command:
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$ dms 10000 4 4 -2.0 > dms_10000_4_4_-2.0.txt
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will produce the desired network. In fact, the average degree of the
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graph will be:
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<k> = 2m = 8
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and the exponent of the power-law degree distribution will be:
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gamma = 3.0 + a/m = 3.0 -0.5 = 2.5
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The following command:
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$ dms 10000 3 5 0 > dms_10000_3_5_0.txt
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creates a scale-free graph with <N=10000> nodes, where each new node
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creates <m=3> new edges and the initial seed network is a ring of
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<n0=5> nodes. The degree distribution of the final graph will have
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exponent equal to `gamma = 3.0 + a/m = 3.0`. In this case, `dms`
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produces a Barabasi-Albert graph (see ba(1) for details). The edge
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list of the graph is saved in the file `dms_10000_3_5_0.txt` (thanks
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to the redirection operator `>`).
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## SEE ALSO
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ba(1), bb_fitness(1)
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## REFERENCES
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* S\. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin. "Structure of
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Growing Networks with Preferential Linking". Phys. Rev. Lett. 85
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(2000), 4633-4636.
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* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Chapter 6, Cambridge University Press
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(2017)
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* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Appendix 13, Cambridge University Press
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(2017)
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## AUTHORS
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(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`.
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