### Abstract

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.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Microeconomics |

Number of pages | 14 |

Volume | 2007-008 |

Publication status | Published - 2007 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2007-008 |

### Keywords

- Random intersection graphs
- degree distribution
- power law distri- bution
- clustering
- social networks

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## Cite this

Deijfen, M., & Kets, W. (2007).

*Random Intersection Graphs with Tunable Degree Distribution and Clustering*. (CentER Discussion Paper; Vol. 2007-008). Microeconomics.