# Random Intersection Graphs with Tunable Degree Distribution and Clustering

M. Deijfen, W. Kets

Research output: Working paperDiscussion paperOther research output

## 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 Tilburg Microeconomics 14 2007-008 Published - 2007

### Publication series

Name CentER Discussion Paper 2007-008

## Keywords

• Random intersection graphs
• degree distribution
• power law distri- bution
• clustering
• social networks
{"ft_lang_label":"__label__en","ft_lang_prob":0.9013909,"math_prob":0.62343264,"size":1411,"snap":"2020-45-2020-50","text_gpt3_token_len":304,"char_repetition_ratio":0.11656006,"word_repetition_ratio":0.0,"special_character_ratio":0.23033309,"punctuation_ratio":0.13983051,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97974885,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-01T05:40:51Z\",\"WARC-Record-ID\":\"<urn:uuid:d17a7475-c176-4c52-a06b-c402cd6cb768>\",\"Content-Length\":\"46919\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1c05a916-ab0c-4db1-aaf1-fd89e6b81815>\",\"WARC-Concurrent-To\":\"<urn:uuid:741bcffa-6581-4720-804b-9be86484a2dc>\",\"WARC-IP-Address\":\"34.253.178.11\",\"WARC-Target-URI\":\"https://research.tilburguniversity.edu/en/publications/random-intersection-graphs-with-tunable-degree-distribution-and-c/\",\"WARC-Payload-Digest\":\"sha1:GERUABRNPAFKRGLPEEWWOPOL3RPAZLT2\",\"WARC-Block-Digest\":\"sha1:UXDFIK6CTQBNPJTVC5NGSLCKMV4BLIST\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141652107.52_warc_CC-MAIN-20201201043603-20201201073603-00424.warc.gz\"}"}