150 citations · 905 across the 15 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…
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…