Abstract
This paper addresses the issue of measuring temporal dynamics of complex socio-economic relational systems, represented as time-dependent networks. Network dynamics is first splitted into a structural component, accounting for changes in the network topology, and a non-structural component, accounting for permutation of vertex labels. A quantitative measure of the dynamics and its components is then proposed and it is shown how it can be used to investigate and interpret the time evolution of networks. A real example is discussed, pertaining to the dynamics of a subnetwork of the Italian corporate board network.
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Notes
For sake of simplicity, in the following elements of \(X\) partially ordered by \(\le \) will be referred directly as elements of \(P\).
A chain between two nodes \(a\) and \(b\) is called maximal if it is not properly contained in any other chain connecting the two nodes.
The length of a chain is the number of elements of the chain minus 1.
We stress that the proof of the lemma depends upon the properties of the selected metric and the topology of \(\mathbb G _n\) (which, as already stated, has the structure of a lattice of subsets) and that it does not hold for arbitrary metrics and arbitrary lattices.
\(G^{*}\) is turned into \(G_{2}\) permuting vertices \(a\) and \(d\).
Company names are coded as follows: a—Buzzi Unicem; b—Camfin; c—Cobra Automotive Technologies; d—Credito Artigiano; e—Fastweb; f—Fondiaria Sai; g—Saras; h— L’Espresso; i—Indesit; j—Seat Pagine Gialle.
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Fattore, M., Grassi, R. Measuring dynamics and structural change of time-dependent socio-economic networks. Qual Quant 48, 1821–1834 (2014). https://doi.org/10.1007/s11135-013-9861-1
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DOI: https://doi.org/10.1007/s11135-013-9861-1