Detecting degree symmetries in networks
Data Analysis, Statistics and Probability
2007-05-23 v1 Physics and Society
Abstract
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping degree sequences. These measures are evaluated on artificial and real networks. Specifically we consider vertices in the human metabolic network. We also measure the average degree-symmetry coefficient for different classes of real-world network. We find that most studied examples are weakly positively degree-symmetric. The exceptions are an airport network (having a negative degree-symmetry coefficient) and one-mode projections of social affiliation networks that are rather strongly degree-symmetric.
Cite
@article{arxiv.physics/0605029,
title = {Detecting degree symmetries in networks},
author = {Petter Holme},
journal= {arXiv preprint arXiv:physics/0605029},
year = {2007}
}