Message-ID: <1625221785.7023.1575583072017.JavaMail.confluence@wiki.cns.iu.edu> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_7022_1014293734.1575583072016" ------=_Part_7022_1014293734.1575583072016 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Watts Strogatz Clustering Coefficient over K

# Watts Strogatz Clustering Coefficient over K

###### Desc= ription
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Study of the correlation between the clustering coefficient (defined a l= a Watts-Strogatz) and the degree of the nodes of a network. The correlation= is expressed through the function c(k), which represents the aver= age clustering coefficient of all nodes with degree k.

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###### Pros &= Cons
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The network to analyze must be undirected, otherwise there are no specia= l constraints.

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###### Application= s
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The correlation function c(k) can help to identify hierarchical= organization in networks.

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###### Im= plementation Details
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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 for the binned correlation function = described below. A first read-in of the inputfile will set the values of th= e number of nodes and edges of the network. In the second read-in the degre= e of all nodes is calculated and the edges are stored in an array. Then the= clustering coefficients for all nodes are calculated. The program generate= s one output file, corresponding to the binned correlation functio= n, i.e. the interval spanned by the values of the degree is divided into bi= ns whose size grows while going to higher values of the variable. The size = of each bin is obtained by multiplying by a fixed number the size of the pr= evious bin. The program calculates the average clustering coefficient of no= des whose degree falls within each bin. Because of the different sizes of t= he bins, these averages must be divided by the respective bin size, to have= consistent results.
This technique is particularly suitable to study s= kewed correlation functions: the fact that the size of the bins grows large= for large values of the degree compensates for the fact that not many node= s have high degrees, so it suppresses the fluctuations that one would obser= ve by using bins of equal size. On a double logarithmic scale, which is ver= y useful to determine the possible power law behavior of the correlation fu= nction, the points of the latter will appear equally spaced on the x-axis.<= br> The algorithm runs in a time , where is the number of nodes of the netw= ork and is the average degree squared.

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###### Usage Hints=20 A simple application of this algorithm could be to calculate c(k) for networks created by the modeling algorithms of the NWB. For instance= , the inputfile can be created through the Barabasi-Albert model.=20 Links=20 =20 Source Code=20 =20 Acknowl= edgements=20 The algorithm was implemented and documented by S. Fortunato, integrated= by S. Fortunato and W. Huang.=20 References=20 Vazquez, A., Pastor-Satorras, R., Vespignani, A. (2002) Large-scale topological and dynamical properties o= f Internet Physical Review E 65:066130.=20 See Also= =20 The license could not be verified: License Certificate has expired!=20 Generate a Free license now.
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