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## Technical Report Details

 Date 6-4-2006 Number DISI-TR-06-06 Title Highly Clustered Networks with Preferential Attachment to Close Nodes Authors Matteo Dell'Amico Bibtex Entry E-mail dellamico@disi.unige.it Link http://www.disi.unige.it/person/DellamicoM/research/papers/pa-clustering.pdf Abstract We analyse the properties of networks formed using a variant of the preferential attachment algorithm introduced by Barabási and Albert, where a new node i connects to the old node j with a probability that is proportional to its degree k_j. In our model, nodes are assigned a random position on a ring, and connection probability is proportional to (k_j)^{\alpha}/(d_{ij})^{\sigma}, where d_{ij} is the distance between i and j, and \alpha and \sigma are positive parameters. When \gamma=\sigma/\alpha is fixed and \alpha grows to infinity, an even simpler model selecting the m nodes having the highest value of k_j/(d_{ij})^{\gamma} is produced. The resulting family of networks shows various properties, most interestingly scale-free, small-world, and hierarchical structure, that are commonly found in real-world networks.
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