This paper investigates ultrafilters in the context of connectivity systems, defined as pairs
$(X, f) $ where $ X $ is a finite set and $ f $ is a symmetric submodular function. Ultrafilters …

Although large social and information networks are often thought of as having hierarchical or
tree-like structure, this assumption is rarely tested. We have performed a detailed empirical …

Hyperbolicity is a property of a graph that may be viewed as a “soft” version of a tree, and
recent empirical and theoretical work has suggested that many graphs arising in Internet …

Based on solid theoretical foundations, we present strong evidence that a number of real‐
world networks, taken from different domains (such as Internet measurements, biological …

Network measures that reflect the most salient properties of complex large-scale networks
are in high demand in the network research community. In this paper we adapt a …

To achieve fast recovery from link failures, most modern communication networks feature
local fast failover mechanisms in the data plane. These failover mechanisms typically rely on …

Modern communication networks feature local fast failover mechanisms in the data plane, to
swiftly respond to link failures with pre-installed rerouting rules. This paper explores resilient …

We investigate the impact the negative curvature has on the traffic congestion in large-scale
networks. We prove that every Gromov hyperbolic network G admits a core, thus answering …

A graph is called $\alpha_i $-metric ($ i\in {\cal N} $) if it satisfies the following $\alpha_i $-
metric property for every vertices $ u, w, v $ and $ x $: if a shortest path between $ u $ and …

Recent work has established that large informatics graphs such as social and information
networks have non-trivial tree-like structure when viewed at moderate size scales. Here, we …