Related papers: Testing for the Network Small-World Property
This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or…
The famous Watts-Strogatz (WS) small-world network model does not approach the Erd\H{o}s-R\'enyi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we…
We consider a standard \textit{susceptible-infected-susceptible} (SIS) model to study behaviors of steady states of epidemic spreading in small-world networks. Using analytical methods and large scale simulations, we recover the usual…
Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are,…
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
Traceroute measurements are one of our main instruments to shed light onto the structure and properties of today's complex networks such as the Internet. This paper studies the feasibility and infeasibility of inferring the network topology…
In order to detect patterns in real networks, randomized graph ensembles that preserve only part of the topology of an observed network are systematically used as fundamental null models. However, their generation is still problematic. The…
We consider single-particle quantum transport on parametrized complex networks. Based on general arguments regarding the spectrum of the corresponding Hamiltonian, we derive bounds for a measure of the global transport efficiency defined by…
Recent empirical work [Leskovec2009] has suggested the existence of a size threshold for the existence of clusters within many real-world networks. We give the first proof that this clustering size threshold exists within a real-world…
The "small-world effect" is the observation that one can find a short chain of acquaintances, often of no more than a handful of individuals, connecting almost any two people on the planet. It is often expressed in the language of networks,…
A classic experiment by Milgram shows that individuals can route messages along short paths in social networks, given only simple categorical information about recipients (such as "he is a prominent lawyer in Boston" or "she is a Freshman…
This paper introduces new techniques for sampling attributed networks to support standard Data Mining tasks. The problem is important for two reasons. First, it is commonplace to perform data mining tasks such as clustering and…
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…
Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…
A classic experiment by Milgram shows that individuals can route messages along short paths in social networks, given only simple categorical information about recipients (such as "he is a prominent lawyer in Boston" or "she is a Freshman…
We introduce the \emph{idemetric} property, which formalises the idea that most nodes in a graph have similar distances between them, and which turns out to be quite standard amongst small-world network models. Modulo reasonable sparsity…
Rich-club, assortativity and clustering coefficients are frequently-used measures to estimate topological properties of complex networks. Here we find that the connectivity among a very small portion of the richest nodes can dominate the…
A database of minima and transition states corresponds to a network where the minima represent nodes and the transition states correspond to edges between the pairs of minima they connect via steepest-descent paths. Here we construct…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
The clustering coefficient, path length and average vertex degree of two urban train line networks have been calculated. The results are compared with theoretical predictions for appropriate random bipartite graphs. They have also been…