Mathematics – Combinatorics
Scientific paper
2012-01-13
Mathematics
Combinatorics
Scientific paper
When comparing networks (with the same number of nodes) with direct methods, a number of possible distances is already available in literature. Among others, two of the most common families are the set of edit-like distances and the spectral distances. The functions in the former family quantitatively evaluate the differences between two networks in terms of minimum number of edit operations (with possibly different costs) transforming one network into the other, that is, deletion and insertion of links, while spectral measures relies on functions of the eigenvalues of one of the connectivity matrices of the underlying graph. A noticeable issue affecting edit distance is the fact of being local, i.e. not taking into account the global structure of the networks but only summing the contributions coming from each single link. On the other hand, spectral measures cannot distinguish isomorphic or isospectral graphs. We propose here a possible solution to overcome both issues: combining together an edit and a spectral distance in a product metric we will define \textit{glocal}. In what follows we define the two components and the glocal metric itself, with a few examples of applications.
Filosi Michele
Furlanello Cesare
Jurman Giuseppe
Riccadonna Samantha
Visintainer Roberto
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