The algorithm builds the histogram of the values of the outdegree of all= nodes, which will be delivered in the two output files.

=20The network to analyze must be directed, otherwise there are no special = constraints.

=20Basic analysis tool, not particular for special disciplines or problems.=

=20The algorithm requires two inputs, the file where the edges of the netwo=
rk are listed and the number of points one wishes to have in the binned dis=
tribution described below. A first read-in of the inputfile will set the va=
lues of the number of nodes and edges of the network. In the second read-in=
the outdegrees of all nodes will be calculated. Then the distribution is c=
alculated.

The program generates two output files, corresponding to two=
different ways of partitioning the interval spanned by the values of outde=
gree. In the first output, the occurrence of any outdegree value between th=
e minimum and the maximum is estimated and divided by the number of nodes o=
f the network, so to obtain the probability: the output displays all outdeg=
ree values in the interval with their probabilities.

The second output =
gives the *binned* distribution, i.e. the interval spanned by the va=
lues of outdegree is divided into bins whose size grows while going to high=
er values of the variable. The size of each bin is obtained by multiplying =
by a fixed number the size of the previous bin. The program calculates the =
fraction of nodes whose outdegree falls within each bin. Because of the dif=
ferent sizes of the bins, these fractions must be divided by the respective=
bin size, to have meaningful averages.

This technique is particularly =
suitable to study skewed distributions: the fact that the size of the bins =
grows large for large outdegree values compensates for the fact that not ma=
ny nodes have high outdegree values, so it suppresses the fluctuations that=
one would observe by using bins of equal size. On a double logarithmic sca=
le, which is very useful to determine the possible power law behavior of th=
e distribution, the points of the latter will appear equally spaced on the =
x-axis.

The program runs in a time O(m), m being the number of edges of=
the network.

- =20
- Source Code =20

The algorithm was implemented and documented by S. Fortunato, integrated= by S. Fortunato and W. Huang.

=20Bollobas, B. (2002) Modern Graph Theory. Springer Verlag, New York.

= =20Albert, R., and Barabasi, A.-L. (2002) Statistical mechanics of complex networks. Review of Modern Phys= ics 74:47-97.

=20Newman, M.E.J. (2003) Th= e structure and function of complex networks. SIAM Review 45:167-256.=20

Pastor-Satorras, R., Vespignani, A. (2004) Evolution and Structure of th= e Internet. Cambridge University Press.

=20Boccaletti, S., Latora, V., Moreno, Y.,Chavez, M., Hwang, D.-U. (2006) <= a href=3D"http://www.ct.infn.it/%7Elatora/report_06.pdf" class=3D"external-= link" rel=3D"nofollow">Complex networks: Structure and dynamics. Physic= s Reports 424: 175-308.

=20
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