From 3aee2fd43e3059a699af2b63c6f2395e5a55e515 Mon Sep 17 00:00:00 2001 From: KatolaZ Date: Wed, 27 Sep 2017 15:06:31 +0100 Subject: First commit on github -- NetBunch 1.0 --- doc/dms.1.html | 183 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 183 insertions(+) create mode 100644 doc/dms.1.html (limited to 'doc/dms.1.html') diff --git a/doc/dms.1.html b/doc/dms.1.html new file mode 100644 index 0000000..e51aa79 --- /dev/null +++ b/doc/dms.1.html @@ -0,0 +1,183 @@ + + + + + + dms(1) - Grow a scale-free random graph with tunable exponent + + + + + +
+ + + +
    +
  1. dms(1)
    2. +
  2. www.complex-networks.net
    3. +
  3. dms(1)
    4. +
+ +

NAME

+

+ dms - 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

+ + + + +

AUTHORS

+ +

(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.

+ + +
    +
  1. www.complex-networks.net
    2. +
  2. September 2017
    3. +
  3. dms(1)
    4. +
+ +
+ + -- cgit v1.2.3