Related papers: The missing links in the BGP-based AS connectivity…
Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Unfortunately, our maps of most large networks are…
The algebraic connectivity of a network characterizes the lower-bound of the exponential convergence rate of consensus processes. This paper investigates the problem of accelerating the convergence of consensus processes by adding links to…
The goal of this work is to model the peering arrangements between Autonomous Systems (ASes). Most existing models of the AS-graph assume an undirected graph. However, peering arrangements are mostly asymmetric Customer-Provider…
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…
We study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps, interacting with random delay times. Four different types of topologies are investigated: two regular (a ring-type and a…
In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization…
Given a finite set T of maps on a finite ring R, we look at the finite simple graph G=(V,E) with vertex set V=R and edge set E={(a,b) | exists t in T, b=t(a), b not equal to a}. An example is when R=Z_n and T consists of a finite set of…
A comparison between the topological properties of the measured Internet topology, at the autonomous system level (AS graph), and the equivalent graphs generated by two different power law topology generators is presented. Only one of the…
For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a…
We consider the $k$-core decomposition of network models and Internet graphs at the autonomous system (AS) level. The $k$-core analysis allows to characterize networks beyond the degree distribution and uncover structural properties and…
The study of SIS epidemics on networks has stressed the role of the network topology on the spreading process. However, accurate models of SIS epidemics rely on the complete knowledge of the network topology, which is often not available.…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
We introduce the concept of matching connectivity as a notion of connectivity in graph admitting perfect matchings which heavily relies on the structural properties of those matchings. We generalise a result of Robertson, Seymour and Thomas…
We numerically investigate the scale-free network model of Barab{\'a}si and Albert [A. L. Barab{\'a}si and R. Albert, Science {\bf 286}, 509 (1999)] through the use of various path finding strategies. In real networks, global network…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
There are a number of existing studies analysing the convergence behaviour of graph neural networks on large random graphs. Unfortunately, the majority of these studies do not model correlations between node features, which would naturally…
The Border Gateway Protocol (BGP) is a distributed protocol that manages interdomain routing without requiring a centralized record of which autonomous systems (ASes) connect to which others. Many methods have been devised to infer the AS…
A massive and growing part of Autonomous System (AS)-level traffic exchanges takes place at Internet Exchange Points (IXPs). This paper leverages PeeringDB, a database providing a partial but reasonable view of the global interconnection of…
During the last three decades the Internet has experienced fascinating evolution, both exponential growth in traffic and rapid expansion in topology. The size of the Internet becomes enormous, yet the network is very `small' in the sense…