In multiplex networks, cycles cannot be characterized only by their length, as edges may occur in different layers in different combinations. We define a classification of cycles by the number of edges in each layer and the number of switches between layers. We calculate the expected number of cycles of each type in the configuration model of a large sparse multiplex network. Our method accounts for the full degree distribution including correlations between degrees in different layers. In particular, we obtain the numbers of cycles of length 3 of all possible types. Using these, we give a complete set of clustering coefficients and their expected values. We show that correlations between the degrees of a vertex in different layers strongly affect the number of cycles of a given type, and the number of switches between layers. Both increase with assortative correlations and are strongly decreased by disassortative correlations. The effect of correlations on clustering coefficients is equally pronounced.

Bootstrap percolation is a simple but nontrivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single-layer (simplex) networks, it has been recently ...

Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several ...

Multiplex networks describe a large variety of complex systems, including infrastructures, transportation networks, and biological systems. Most of these networks feature a significant link overlap. It is therefore of ...

Fennell, Peter G.; Gleeson, James P.; Cellai, Davide(American Physical Society, 2014)

Facilitated spin models were introduced some decades ago to mimic systems characterized by a glass transition. Recent developments have shown that a class of facilitated spin models is also able to reproduce characteristic ...

k-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analyzing the resilience of a network under random damage, an extension of this model ...