Signal propagation in complex networks drives epidemics, is responsible for information
going viral, promotes trust and facilitates moral behavior in social groups, enables the …

Percolation is the simplest fundamental model in statistical mechanics that exhibits phase
transitions signaled by the emergence of a giant connected component. Despite its very …

We investigate the vulnerabilities of consensus-based distributed optimization protocols to
nodes that deviate from the prescribed update rule (eg, due to failures or adversarial …

We derive rigorous asymptotic results for the magnitude of contagion in a large counterparty
network and give an analytical expression for the asymptotic fraction of defaults, in terms of …

Graph matching is a generalization of the classic graph isomorphism problem. By using only
their structures a graph-matching algorithm finds a map between the vertex sets of two …

In $ r $-neighbour bootstrap percolation on a graph $ G $, a (typically random) set $ A $ of
initially 'infected'vertices spreads by infecting (at each time step) vertices with at least $ r …

Consider a linear time-invariant (LTI) dynamical system monitored by a network of sensors,
modeled as nodes of an underlying directed communication graph. We study the problem of …

We consider a graph-theoretic property known as r-robustness which plays a key role in a
class of consensus (or opinion) dynamics where each node ignores its most extreme …

In many graph--mining problems, two networks from different domains have to be matched.
In the absence of reliable node attributes, graph matching has to rely on only the link …

In the continuum, close connections exist between mean curvature flow, the Allen-Cahn
(AC) partial differential equation, and the Merriman-Bence-Osher (MBO) threshold dynamics …