1. bb_fitness(1)
2. www.complex-networks.net
3. bb_fitness(1)

## NAME

`bb_fitness` - 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).

• 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>`.

1. www.complex-networks.net
2. September 2017
3. bb_fitness(1)