Dresden 2003 – wissenschaftliches Programm
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AKSOE: Physik sozio-ökonomischer Systeme
AKSOE 9: Soziale Systeme und Entscheidungsmodelle
AKSOE 9.4: Vortrag
Donnerstag, 27. März 2003, 11:00–11:30, BAR/205
Use of Hermitian matrices in the analysis of newsgroups — •Bettina Hoser and Andreas Geyer-Schulz — Lehrstuhl f. Informationsdienste u. elektron. Maerkte; Universitaet Karlsruhe (TH); 76128 Karlsruhe
Classical network analysis uses adjacency matrices as one of the basic analysis tools. These non–symmetric, non–negative, quadratic matrices A=aij ∈ R contain in their standard version only binary (aij=0 no linkage, aij=c;c ≥ 0 linkage) and thus very basic information about the relationship within the group. The implication is that the resulting eigensystem analysis is a mixture of ’signal’ and ’noise’ (random communication) which is difficult to interpret. Especially, identification of the relevant substructures (informal groups of newsgroup members) in the newsgroup becomes problematic. In this paper we present an enhanced way of describing a network, e.g. for a small newsgroup (90 ≤ N ≤ 150), by a Hermitian matrix. The approach is based on the assumption, that in a newsgroup not only the fact, but also the traffic size and traffic direction with which the members contact each other is essential when analysing the behaviour within the group. We propose a way to incorporate this directed two–way information into a complex, square adjacency matrix M (with mkl=i*mlk*;mkk=0;mkl ∈ C). After rotation by − π/4 the originally non–symmetric complex adjacency matrix becomes Hermitian. The resulting Eigensystem offers on the one hand an Eigenvalue (λr ∈ R) ranking based on the strength (amount of traffic) within a substructure that is centered around a very busy center–person and on the other hand more information about its members.