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Emergence of coexisting percolating clusters in networks
Ali Faqeeh, Sergey Melnik, Pol Colomer-de-Simón +1
It is commonly assumed in percolation theories that at most one percolating cluster can exist in a network. We introduce sausage-like networks (SLNs), an ensemble of synthetic modu…
Analytical approach to the dynamics of facilitated spin models on random networks
Peter G. Fennell, James P. Gleeson, Davide Cellai
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 model…
Singularities in ternary mixtures of k-core percolation
Davide Cellai, James P. Gleeson
Heterogeneous k-core percolation is an extension of a percolation model which has interesting applications to the resilience of networks under random damage. In this model, the not…
Critical phenomena in heterogeneous k-core percolation
Davide Cellai, Aonghus Lawlor, Kenneth A. Dawson +1
-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analysing the resilience of a network und…
Tricritical point in heterogeneous k-core percolation
Davide Cellai, Aonghus Lawlor, Kenneth A. Dawson +1
k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understand the resilience of complex networks under random damage. A new…
The unreasonable effectiveness of tree-based theory for networks with clustering
Sergey Melnik, Adam Hackett, Mason A. Porter +2
We demonstrate that a tree-based theory for various dynamical processes yields extremely accurate results for several networks with high levels of clustering. We find that such a t…