Detecting degree symmetries in networks

Details Detecting degree symmetries in networks Detecting degree symmetries in networks

2006-05-03

arxiv.org/abs/physics/0605029v1

Phys. Rev. E 74, 036107 (2006)

Physics

Data Analysis, Statistics and Probability

Scientific paper

10.1103/PhysRevE.74.036107

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.

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