A random intersection graph is constructed by independently assigning each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in which each vertex is given a random weight, and vertices with larger weights are more likely to be assigned large subsets. The distribution of the degree of a given vertex is determined and is shown to depend on the weight of the vertex. In particular, if the weight distribution is a power law, the degree distribution will be so as well. Furthermore, an asymptotic expression for the clustering in the graph is derived. By tuning the parameters of the model, it is possible to generate a graph with arbitrary clustering, expected degree and { in the power law case { tail exponent.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number
2007-8.
For technical questions regarding this item, or to correct its listing, contact: (Corry Stuyts).
Related research
Keywords:
Find related papers by JEL classification: C65 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Miscellaneous Mathematical Tools Z13 - Other Special Topics - - Cultural Economics - - - Social Norms and Social Capital; Social Networks Economic Anthropology
This paper has been announced in the following NEP Reports: