150 citations · 905 across the 15 of their papers we have counts for
15 papers
Exact analytical solution of irreversible binary dynamics on networks
Edward Laurence, Jean-Gabriel Young, Sergey Melnik +1
In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), and nodes in the inactive state make an irreversible transition to the active…
A framework for analyzing contagion in assortative banking networks
Thomas R. Hurd, James P. Gleeson, Sergey Melnik
We introduce a probabilistic framework that represents stylized banking networks with the aim of predicting the size of contagion events. Most previous work on random financial net…
Simple and accurate analytical calculation of shortest path lengths
Sergey Melnik, James P. Gleeson
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undir…
The limitations of discrete-time approaches to continuous-time contagion dynamics
Peter G. Fennell, Sergey Melnik, James P. Gleeson
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating c…
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…
Network cloning unfolds the effect of clustering on dynamical processes
Ali Faqeeh, Sergey Melnik, James P. Gleeson
We introduce network -cloning, a technique for creating ensembles of random networks from any given real-world or artificial network. Each member of the ensemble is an -clone…
Double Cascade Model of Financial Crises
Thomas R. Hurd, Davide Cellai, Sergey Melnik +1
The scope of financial systemic risk research encompasses a wide range of interbank channels and effects, including asset correlation shocks, default contagion, illiquidity contagi…
Analytical solution for a class of network dynamics with mechanical and financial applications
Pavel Krejčí, Harbir Lamba, Sergey Melnik +1
We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone inp…
Dynamics on Modular Networks with Heterogeneous Correlations
Sergey Melnik, Mason A. Porter, Peter J. Mucha +1
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint deg…
Multi-Stage Complex Contagions
Sergey Melnik, Jonathan A. Ward, James P. Gleeson +1
The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investiga…
Cascades on a class of clustered random networks
Adam Hackett, Sergey Melnik, James P. Gleeson
We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution a…
Accuracy of Mean-Field Theory for Dynamics on Real-World Networks
James P. Gleeson, Sergey Melnik, Jonathan A. Ward +2
Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field…
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…
How clustering affects the bond percolation threshold in complex networks
James P. Gleeson, Sergey Melnik, Adam Hackett
The question of how clustering (non-zero density of triangles) in networks affects their bond percolation threshold has important applications in a variety of disciplines. Recent a…
Analytical results for bond percolation and k-core sizes on clustered networks
James P. Gleeson, Sergey Melnik
An analytical approach to calculating bond percolation thresholds, sizes of -cores, and sizes of giant connected components on structured random networks with non-zero clusterin…