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.TH "BB_FITNESS" "1" "September 2017" "www.complex-networks.net" "www.complex-networks.net"
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.SH "NAME"
\fBbb_fitness\fR \- Grow a random graph with the fitness model
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.SH "SYNOPSIS"
\fBbb_fitness\fR \fIN\fR \fIm\fR \fIn0\fR [SHOW]
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.SH "DESCRIPTION"
\fBbb_fitness\fR grows an undirected random scale\-free graph with \fIN\fR nodes using the fitness model proposed by Bianconi and Barabasi\. The initial network is a clique of \fIn0\fR nodes, and each new node creates \fIm\fR new edges\. The probability that a new node create an edge to node \fBj\fR is proportional to
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.IP "" 4
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.nf

    a_j * k_j
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.fi
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.IP "" 0
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.P
where \fBa_j\fR is the attractiveness (fitness) of node \fBj\fR\. The values of node attractiveness are sampled uniformly in the interval [0,1]\.
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.SH "PARAMETERS"
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.TP
\fIN\fR
Number of nodes of the final graph\.
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.TP
\fIm\fR
Number of edges created by each new node\.
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.TP
\fIn0\fR
Number of nodes in the initial (seed) graph\.
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.TP
SHOW
If the fourth parameter is equal to \fBSHOW\fR, the values of node attractiveness are printed on STDERR\.
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.SH "OUTPUT"
\fBbb_fitness\fR prints on STDOUT the edge list of the final graph\.
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.SH "EXAMPLES"
The following command:
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.IP "" 4
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.nf

    $ bb_fitness 10000 3 4 > bb_fitness_10000_3_4\.txt
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.fi
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.IP "" 0
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.P
uses the fitness model to create a random graph with \fIN=10000\fR nodes, where each new node creates \fIm=3\fR new edges and the initial seed network is a ring of \fIn0=5\fR nodes\. The edge list of the resulting graph is saved in the file \fBbb_fitness_10000_3_4\.txt\fR (notice the redirection operator \fB>\fR)\. The command:
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.IP "" 4
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.nf

    $ bb_fitness 10000 3 4 SHOW > bb_fitness_10000_3_4\.txt 2> bb_fitness_10000_3_4\.txt_fitness
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.fi
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.IP "" 0
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.P
will do the same as above, but it will additionally save the values of node fitness in the file \fBbb_fitness_10000_3_4\.txt_fitness\fR (notice the redirection operator \fB2>\fR, that redirects the STDERR to the specified file)\.
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.SH "SEE ALSO"
ba(1), dms(1)
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.SH "REFERENCES"
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.IP "\(bu" 4
G\. Bianconi, A\.\-L\. Barabasi, " Competition and multiscaling in evolving networks"\. EPL\-Europhys\. Lett\. 54 (2001), 436\.
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.IP "\(bu" 4
V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 6, Cambridge University Press (2017)
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.IP "\(bu" 4
V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 13, Cambridge University Press (2017)
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.IP "" 0
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.SH "AUTHORS"
(c) Vincenzo \'KatolaZ\' Nicosia 2009\-2017 \fB<v\.nicosia@qmul\.ac\.uk>\fR\.