# Distribution and Dependence of Extremes in Network Sampling Processes

1 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We explore the dependence structure in the sampled sequence of complex networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers or income of the nodes in Online Social Networks etc, which satisfy two mixing conditions. Several useful extremes of the sampled sequence like $k$th largest value, clusters of exceedances over a threshold, first hitting time of a large value etc are investigated. We abstract the dependence and the statistics of extremes into a single parameter that appears in Extreme Value Theory, called extremal index (EI). In this work, we derive this parameter analytically and also estimate it empirically. We propose the use of EI as a parameter to compare different sampling procedures. As a specific example, degree correlations between neighboring nodes are studied in detail with three prominent random walks as sampling techniques.
Keywords :
Type de document :
Communication dans un congrès
3rd International Workshop on Complex Networks and their Applications (COMPLEX NETWORKS 2014), Nov 2014, Marrakech, Morocco. pp.331-338, 〈http://www.complexnetworks.org/index.html〉
Domaine :

https://hal.inria.fr/hal-01094259
Contributeur : Jithin Sreedharan <>
Soumis le : jeudi 11 décembre 2014 - 23:03:12
Dernière modification le : jeudi 11 janvier 2018 - 16:57:55

### Identifiants

• HAL Id : hal-01094259, version 1

### Citation

Konstantin Avrachenkov, Natalia M. Markovich, Jithin K. Sreedharan. Distribution and Dependence of Extremes in Network Sampling Processes. 3rd International Workshop on Complex Networks and their Applications (COMPLEX NETWORKS 2014), Nov 2014, Marrakech, Morocco. pp.331-338, 〈http://www.complexnetworks.org/index.html〉. 〈hal-01094259〉

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