Message-ID: <1640030103.10689.1561416429239.JavaMail.confluence@wiki.cns.iu.edu> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_10688_1531410631.1561416429238" ------=_Part_10688_1531410631.1561416429238 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Diameter

Diameter

Description
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The Diameter algorithm calculates the length of the longest shortest pat= h between pairs of nodes of a network (diameter). The shortest path lengths= are calculated via breadth-first search.=20

Pros & Cons
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The network to analyze must be undirected, otherwise there are no specia= l 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 Details
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The algorithm needs only one input, the file where the edges of the netw= ork are listed. A first read-in of the inputfile will set the values of the= number of nodes and edges of the network. In the second read-in the edges = are stored in an array. Then the breadth-first search process is performed = and the histogram of the shortest path length is evaluated. From the latter= the diameter is determined and displayed in the NWB console. The algorithm= runs in a time O(nm), where n is the number of nodes, m the number of edges of the network. This algorithm is particularly= suitable for sparse networks, i.e. if m n; in that case, the computation= al complexity is O(n^2). Because of the quadratic dependence on th= e number of nodes, the algorithm should not be applied to networks with mor= e than 10^5 nodes.

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Usage Hints
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A simple application of this algorithm could be to calculate the diamete= r for networks created by the modeling algorithms of the NWB. For instance,= the inputfile can be created through the Barabasi-Albert model.

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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. For the description we acknowledge Wikipedia= .

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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.(2002) Evolution and Structure of the= Internet. Cambridge University Press.

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Boccaletti, S., Latora, V., Moreno, Y.,Chavez, M., Hwang, D.-U.(2006) Complex networks: Structure and dynamics. Physics= Reports 424: 175-308.

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