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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 11: Social, Information and Production Networks II

AKSOE 11.1: Vortrag

Dienstag, 8. März 2005, 14:00–14:30, TU P-N203

Complete decomposition of communication patterns social networks: an approach based on complex Hermitian adjacency matrices — •Bettina Hoser and Andreas Geyer-Schulz — Lehrstuhl f. Informationsdienste u. elektronische Märkte, Universität Karlsruhe (TH), Zirkel 2, 76131 Karlsruhe

In this paper the method of eigensystem analysis of complex Hermitian adjacency matrices is used to describe asymmetric communication patterns in social networks. As an example a well known data set (EIES data set) is analyzed.

The eigensystem of the complex Hermitian adjacency matrix is such, that it offers a decomposition of the original matrix into all detectable patterns and groups. The eigenvalues represent the relative amount of traffic volume being communicated in a pattern, while the sign of the eigenvalue helps to identify patterns that exist within a subgroup and as well as between this subgroup and the rest of the network. The distribution of eigenvalues yields information about the overall structure of communication.

The absolute value of the eigenvector components give information about the relevance of different network members within any of the detected patterns. The phase information of the eigenvector component gives the additional information about directional preference of communication in that pattern.

Also an outlook on other applications will be given. Preliminary results show that forecasting markets, like political stock markets, can be analyzed in structure as well as prognostic quality by this method.