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diff --git a/doc/bb_fitness.md b/doc/bb_fitness.md new file mode 100644 index 0000000..7e97107 --- /dev/null +++ b/doc/bb_fitness.md @@ -0,0 +1,80 @@ +bb_fitness(1) -- Grow a random graph with the fitness model +====== + +## SYNOPSIS + +`bb_fitness` <N> <m> <n0> [SHOW] + +## DESCRIPTION + +`bb_fitness` grows an undirected random scale-free graph with <N> +nodes using the fitness model proposed by Bianconi and Barabasi. The +initial network is a clique of <n0> nodes, and each new node creates +<m> new edges. The probability that a new node create an edge to node +`j` is proportional to + + a_j * k_j + +where `a_j` is the attractiveness (fitness) of node `j`. The values of +node attractiveness are sampled uniformly in the interval [0,1]. + +## 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. + +* SHOW: + If the fourth parameter is equal to `SHOW`, the values of node + attractiveness are printed on STDERR. + +## OUTPUT + +`bb_fitness` prints on STDOUT the edge list of the final graph. + +## EXAMPLES + +The following command: + + $ bb_fitness 10000 3 4 > bb_fitness_10000_3_4.txt + +uses the fitness model to create a random 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 edge list of the resulting +graph is saved in the file `bb_fitness_10000_3_4.txt` (notice the +redirection operator `>`). The command: + + $ bb_fitness 10000 3 4 SHOW > bb_fitness_10000_3_4.txt 2> bb_fitness_10000_3_4.txt_fitness + +will do the same as above, but it will additionally save the values of +node fitness in the file `bb_fitness_10000_3_4.txt_fitness` (notice +the redirection operator `2>`, that redirects the STDERR to the +specified file). + +## SEE ALSO + +ba(1), dms(1) + +## REFERENCES + +* G\. Bianconi, A.-L. Barabasi, " Competition and multiscaling in + evolving networks". EPL-Europhys. Lett. 54 (2001), 436. + +* 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>`. + |