Holme Petter
Department of Computer Science, University of New Mexico, Albuquerque, New Mexico 87131, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 2):036107. doi: 10.1103/PhysRevE.74.036107. Epub 2006 Sep 14.
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.
网络中一个顶点的周围环境或多或少可以是对称的。我们推导了一种特定类型的顶点对称性度量，我们称之为度对称性——即从一个顶点出发的许多路径具有重叠度序列的性质。这些度量在人工网络和真实网络上进行评估。具体来说，我们考虑人类代谢网络中的顶点。我们还测量了不同类别的真实世界网络的平均度对称系数。我们发现，大多数研究示例的度对称性为弱正相关。例外情况是一个机场网络（具有负度对称系数）和社会归属网络的单模投影，它们的度对称性相当强。
