Measuring the dimension of partially embedded networks

Scaling phenomena have been intensively studied during the past decade in the context of complex networks. As part of these works, recently novel methods have appeared to measure the dimension of abstract and spatially embedded networks. In this paper we propose a new dimension measurement method for networks, which does not require global knowledge on the embedding of the nodes, instead it exploits link-wise information (link lengths, link delays or other physical quantities). Our method can be regarded as a generalization of the spectral dimension, that grasps the network's large-scale structure through local observations made by a random walker while traversing the links. We apply the presented method to synthetic and real-world networks, including road maps, the Internet infrastructure and the Gowalla geosocial network. We analyze the theoretically and empirically designated case when the length distribution of the links has the form P(r) ~ 1/r. We show that while previous dimension concepts are not applicable in this case, the new dimension measure still exhibits scaling with two distinct scaling regimes. Our observations suggest that the link length distribution is not sufficient in itself to entirely control the dimensionality of complex networks, and we show that the proposed measure provides information that complements other known measures

A Bayesian Approach to Identify Bitcoin Users

Bitcoin is a digital currency and electronic payment system operating over a peer-to-peer network on the Internet. One of its most important properties is the high level of anonymity it provides for its users. The users are identified by their Bitcoin addresses, which are random strings in the public records of transactions, the blockchain. When a user initiates a Bitcoin-transaction, his Bitcoin client program relays messages to other clients through the Bitcoin network. Monitoring the propagation of these messages and analyzing them carefully reveal hidden relations. In this paper, we develop a mathematical model using a probabilistic approach to link Bitcoin addresses and transactions to the originator IP address. To utilize our model, we carried out experiments by installing more than a hundred modified Bitcoin clients distributed in the network to observe as many messages as possible. During a two month observation period we were able to identify several thousand Bitcoin clients and bind their transactions to geographical locations

On the network geography of the Internet

Abstract—The geographic layout of the physical Internet inherently determines important network properties and traffic characteristics. To give insight into the geography of the Internet, we examine the spatial properties of the topology and routing. To represent the network we conducted a geographically dispersed traceroute campaign, and embedded the extracted topology into the geographic space by applying a novel IP geolocalization service, called Spotter. In this paper we present the frequency analysis of link lengths, quantify path circuitousness and explore the symmetry of end-to-end Internet routes. I

Spectral correlations in systems undergoing a transition from periodicity to disorder

We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the degree of disorder. It interpolates smoothly between the two extreme limits -- the approach to Poissonian statistics in the (weakly) disordered case, and the universal expressions derived for the periodic case. The theoretical results agree very well with the spectral statistics obtained numerically for chains of chaotic billiards and graphs.Comment: 16 pages, Late