Statistical Analysis of Weighted Networks
The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely, average path length, degree distribution, and clustering coefficient. Although the degree distribution and the average path length admit str...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/375452 |
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| _version_ | 1832558996550057984 |
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| author | I. E. Antoniou E. T. Tsompa |
| author_facet | I. E. Antoniou E. T. Tsompa |
| author_sort | I. E. Antoniou |
| collection | DOAJ |
| description | The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely, average path length, degree distribution, and clustering coefficient. Although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. We examined the different definitions and identified the similarities and differences between them. In order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. For this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. This study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs. |
| format | Article |
| id | doaj-art-55efbc9a915645f582e35f0eae0271e5 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-55efbc9a915645f582e35f0eae0271e52025-02-03T01:30:59ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/375452375452Statistical Analysis of Weighted NetworksI. E. Antoniou0E. T. Tsompa1Mathematics Department, Aristotle University, 54124 Thessaloniki, GreeceMathematics Department, Aristotle University, 54124 Thessaloniki, GreeceThe purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely, average path length, degree distribution, and clustering coefficient. Although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. We examined the different definitions and identified the similarities and differences between them. In order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. For this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. This study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs.http://dx.doi.org/10.1155/2008/375452 |
| spellingShingle | I. E. Antoniou E. T. Tsompa Statistical Analysis of Weighted Networks Discrete Dynamics in Nature and Society |
| title | Statistical Analysis of Weighted Networks |
| title_full | Statistical Analysis of Weighted Networks |
| title_fullStr | Statistical Analysis of Weighted Networks |
| title_full_unstemmed | Statistical Analysis of Weighted Networks |
| title_short | Statistical Analysis of Weighted Networks |
| title_sort | statistical analysis of weighted networks |
| url | http://dx.doi.org/10.1155/2008/375452 |
| work_keys_str_mv | AT ieantoniou statisticalanalysisofweightednetworks AT ettsompa statisticalanalysisofweightednetworks |