Bianconi Ginestra
Département de Physique Théorique, Université de Fribourg Pérolles, CH-1700 Fribourg, Switzerland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 May;67(5 Pt 2):056119. doi: 10.1103/PhysRevE.67.056119. Epub 2003 May 23.
The metric structure of bosonic scale-free networks and fermionic Cayley-tree networks is analyzed, focusing on the directed distance of nodes from the origin. The topology of the networks strongly depends on the dynamical parameter T, called the temperature. At T= infinity we show analytically that the two networks have a similar behavior: the distance of a generic node from the origin of the network scales as the logarithm of the number of nodes in the network. At T=0 the two networks have an opposite behavior: the bosonic network remains very clusterized (the distance from the origin remains constant as the network increases the number of nodes), while the fermionic network grows following a single branch of the tree, and the distance from the origin varies as a power law of the number of nodes in the network.
分析了玻色子无标度网络和费米子凯莱树网络的度量结构，重点关注节点到原点的有向距离。网络的拓扑结构强烈依赖于被称为温度的动态参数T。在T = ∞时，我们通过分析表明这两种网络具有相似的行为：网络中一般节点到原点的距离与网络中节点数量的对数成比例。在T = 0时，这两种网络具有相反的行为：玻色子网络仍然非常聚集（随着网络节点数量增加，到原点的距离保持不变），而费米子网络沿着树的单个分支增长，并且到原点的距离随网络中节点数量的幂律变化。
