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author | KatolaZ <katolaz@freaknet.org> | 2017-09-27 15:06:31 +0100 |
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committer | KatolaZ <katolaz@freaknet.org> | 2017-09-27 15:06:31 +0100 |
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tree | 58c95505a0906ed9cfa694f9dbd319403fd8f01d /doc/dms.md |
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diff --git a/doc/dms.md b/doc/dms.md new file mode 100644 index 0000000..2969ff5 --- /dev/null +++ b/doc/dms.md @@ -0,0 +1,92 @@ +dms(1) -- Grow a scale-free random graph with tunable exponent +====== + +## SYNOPSIS + +`dms` <N> <m> <n0> _a_ + +## DESCRIPTION + +`dms` grows an undirected random scale-free graph with <N> nodes using +the modified linear preferential attachment model proposed by +Dorogovtsev, Mendes and Samukhin. The initial network is a clique of +<n0> nodes, and each new node creates <m> new edges. The resulting +graph will have a scale-free degree distribution, whose exponent +converges to `gamma=3.0 + a/m` for large <N>. + +## PARAMETERS + +* <N>: + Number of nodes of the final graph. + +* <m>: + Number of edges created by each new node. + +* <n0>: + Number of nodes in the initial (seed) graph. + +* _a_: + This parameter sets the exponent of the degree distribution + (`gamma = 3.0 + a/m`). _a_ must be larger than <-m>. + +## OUTPUT + +`dms` prints on STDOUT the edge list of the final graph. + +## EXAMPLES + +Let us assume that we want to create a scale-free network with +<N=10000> nodes, with average degree equal to 8, whose degree +distribution has exponent + + gamma = 2.5 + +Since `dms` produces graphs with scale-free degree sequences with an +exponent `gamma = 3.0 + a/m`, the command: + + $ dms 10000 4 4 -2.0 > dms_10000_4_4_-2.0.txt + +will produce the desired network. In fact, the average degree of the +graph will be: + + <k> = 2m = 8 + +and the exponent of the power-law degree distribution will be: + + gamma = 3.0 + a/m = 3.0 -0.5 = 2.5 + +The following command: + + $ dms 10000 3 5 0 > dms_10000_3_5_0.txt + +creates a scale-free graph with <N=10000> nodes, where each new node +creates <m=3> new edges and the initial seed network is a ring of +<n0=5> nodes. The degree distribution of the final graph will have +exponent equal to `gamma = 3.0 + a/m = 3.0`. In this case, `dms` +produces a Barabasi-Albert graph (see ba(1) for details). The edge +list of the graph is saved in the file `dms_10000_3_5_0.txt` (thanks +to the redirection operator `>`). + +## SEE ALSO + +ba(1), bb_fitness(1) + +## REFERENCES + +* S\. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin. "Structure of + Growing Networks with Preferential Linking". Phys. Rev. Lett. 85 + (2000), 4633-4636. + +* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, + Methods and Applications", Chapter 6, Cambridge University Press + (2017) + +* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, + Methods and Applications", Appendix 13, Cambridge University Press + (2017) + + +## AUTHORS + +(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`. + |