Message-ID: <1827733900.12533.1606780270441.JavaMail.confluence@wiki.cns.iu.edu> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_12532_1854391199.1606780270440" ------=_Part_12532_1854391199.1606780270440 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Outdegree Distribution

# Outdegree Distribution

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

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###### Pros & Cons
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The network to analyze must be directed, otherwise there are no special = constraints.

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

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###### Implementation Detai= ls
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The 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.

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

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###### References
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Bollobas, B. (2002) Modern Graph Theory. Springer Verlag, New York.

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

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Newman, 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.

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Boccaletti, 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.

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