Detecting degree symmetries in networks.
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.
Holme
Petter
P
Department of Computer Science, University of New Mexico, Albuquerque, New Mexico 87131, USA.
D000465:Algorithms; D001671:Biochemistry / Q000379:methods; D016000:Cluster Analysis; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net; D013096:Spermine / Q000378:metabolism; D049490:Systems Biology
D013096:Spermine