Displaying similar documents to “Spectral Techniques in Complex Networks”

Segmentation in personal networks

Tom A. B. Snijders, Marinus Spreen (1997)

Mathématiques et Sciences Humaines

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A concept and several measures for segmentation of personal networks are proposed. It is argued that the implications of segmentation of personal networks are, in a sense, the opposite of those of segmentation of entire networks. The measures are illustrated by the example of the trust network in a civil service departement. For the case where relations in the personal network are observed by a sample rather than completely, estimators for the segmentation measures are given. ...

Using R to Build and Assess Network Models in Biology

G. Hartvigsen (2011)

Mathematical Modelling of Natural Phenomena

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In this paper we build and analyze networks using the statistical and programming environment R and the igraph package. We investigate random, small-world, and scale-free networks and test a standard problem of connectivity on a random graph. We then develop a method to study how vaccination can alter the structure of a disease transmission network. We also discuss a variety of other uses for networks in biology.

Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory

R. E. Lee DeVille, C. S. Peskin, J. H. Spencer (2010)

Mathematical Modelling of Natural Phenomena

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We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition...