Abstract
A structural metric of a network is a measure of some property directly dependent on the system of relations between the components of the network, i.e., by representing the network with a graph, a structural metric is a measure of a property that depends on the edge set.
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Notes
- 1.
Note that we use the term “cycle” to refer to a walk that starts and ends at the same physical node u. It is permissible (and relevant) to return to the same node via a different layer from the one that was used originally to leave the node.
- 2.
The definition we adopt for the global clustering coefficient is an example of a global structural metric that is not defined as the mean value over all the nodes of its local version. Actually, it is defined as the ratio between the mean number of closed triples and the mean number of open triples.
- 3.
We use the configuration model instead of an ER network as a null model because the local clustering coefficient values are typically correlated with nodes degrees in single layer networks [55], and an ER-network null model would not preserve degree sequence.
- 4.
By induction, \(f(\mathcal {Q}_R(\mathcal {A\widehat {C}}))=\mathcal {Q}_L(f(\widehat {C}\mathcal {A}))\), that is, \(\tilde {\mathbf {K}}=f(\mathbf {W})\)
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Cozzo, E., de Arruda, G.F., Rodrigues, F.A., Moreno, Y. (2018). Structural Metrics. In: Multiplex Networks. SpringerBriefs in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-92255-3_3
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