78,151 research outputs found
The domination number of on-line social networks and random geometric graphs
We consider the domination number for on-line social networks, both in a
stochastic network model, and for real-world, networked data. Asymptotic
sublinear bounds are rigorously derived for the domination number of graphs
generated by the memoryless geometric protean random graph model. We establish
sublinear bounds for the domination number of graphs in the Facebook 100 data
set, and these bounds are well-correlated with those predicted by the
stochastic model. In addition, we derive the asymptotic value of the domination
number in classical random geometric graphs
SPoT: Representing the Social, Spatial, and Temporal Dimensions of Human Mobility with a Unifying Framework
Modeling human mobility is crucial in the analysis and simulation of opportunistic networks, where contacts are exploited as opportunities for peer-topeer message forwarding. The current approach with human mobility modeling has been based on continuously modifying models, trying to embed in them the mobility properties (e.g., visiting patterns to locations or specific distributions of inter-contact times) as they came up from trace analysis. As
a consequence, with these models it is difficult, if not impossible, to modify the features of mobility or to control the exact shape of mobility metrics (e.g., modifying the distribution of inter-contact times). For these reasons, in this paper we propose a mobility framework rather than a mobility model, with the explicit goal of providing a exible and controllable tool for modeling mathematically and generating simulatively different possible features of human mobility. Our framework, named SPoT, is able to incorporate the three dimensions - spatial, social, and temporal - of human mobility. The way SPoT does it is by mapping the different social communities of the network into different locations, whose members visit with a configurable temporal pattern. In order to characterize the temporal patterns of user visits to locations and the relative positioning of locations based on their shared users, we analyze the traces of real user movements extracted from three location-based online social networks (Gowalla, Foursquare, and Altergeo). We observe that a Bernoulli process effectively approximates user visits to locations in the majority of cases and that locations that share many common users visiting them frequently tend to be located close to each other. In addition, we use these traces to test the exibility of the framework, and we show that SPoT is able to accurately reproduce the mobility behavior observed in traces. Finally, relying on the Bernoulli assumption for arrival processes, we provide a throughout mathematical analysis of the controllability of the framework, deriving the conditions under which heavy-tailed and exponentially-tailed aggregate inter-contact times (often observed in real traces) emerge
Spectral statistics of random geometric graphs
We use random matrix theory to study the spectrum of random geometric graphs,
a fundamental model of spatial networks. Considering ensembles of random
geometric graphs we look at short range correlations in the level spacings of
the spectrum via the nearest neighbour and next nearest neighbour spacing
distribution and long range correlations via the spectral rigidity Delta_3
statistic. These correlations in the level spacings give information about
localisation of eigenvectors, level of community structure and the level of
randomness within the networks. We find a parameter dependent transition
between Poisson and Gaussian orthogonal ensemble statistics. That is the
spectral statistics of spatial random geometric graphs fits the universality of
random matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert
and Watts-Strogatz random graph.Comment: 19 pages, 6 figures. Substantially updated from previous versio
Identifying Infection Sources and Regions in Large Networks
Identifying the infection sources in a network, including the index cases
that introduce a contagious disease into a population network, the servers that
inject a computer virus into a computer network, or the individuals who started
a rumor in a social network, plays a critical role in limiting the damage
caused by the infection through timely quarantine of the sources. We consider
the problem of estimating the infection sources and the infection regions
(subsets of nodes infected by each source) in a network, based only on
knowledge of which nodes are infected and their connections, and when the
number of sources is unknown a priori. We derive estimators for the infection
sources and their infection regions based on approximations of the infection
sequences count. We prove that if there are at most two infection sources in a
geometric tree, our estimator identifies the true source or sources with
probability going to one as the number of infected nodes increases. When there
are more than two infection sources, and when the maximum possible number of
infection sources is known, we propose an algorithm with quadratic complexity
to estimate the actual number and identities of the infection sources.
Simulations on various kinds of networks, including tree networks, small-world
networks and real world power grid networks, and tests on two real data sets
are provided to verify the performance of our estimators
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