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Patterns in Complex Networks via Spectral Analysis

Patterns in Complex Networks via Spectral Analysis

This video was recorded at Joint IAPR International Workshops on Structural and Syntactic Pattern Recognition (SSPR) and Statistical Techniques in Pattern Recognition (SPR), Cesme 2010. Complex networks represent a variety of real-world systems in biology, ecology, society and technology. The study of structural properties of such systems has a tremendous impact in our understanding of their function, organisation and dynamics. Here I present a series of results toward the structural characterisation of complex networks. I start by analysing the centrality of nodes in complex networks and we introduce a measure which accounts for the participation of a node in all subgraphs in the network. This method is used to obtain a universal classification of networks into four topological classes. Then, I will develop a method to characterise the communicability between nodes in a network. The method is illustrated by ranking webpages in WWW and it is compared to other algorithms such as PageRank, SALSA, etc. Using the communicability approach I develop a method to identify overlapped communities in networks. I finalise by extending these ideas to account for general matrix functions.

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