White Douglas R, Kejzar Natasa, Tsallis Constantino, Farmer Doyne, White Scott
Institute of Mathematical Behavioral Sciences, University of California Irvine, Irvine, California 92697, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jan;73(1 Pt 2):016119. doi: 10.1103/PhysRevE.73.016119. Epub 2006 Jan 18.
We propose a model for network formation and study some of its statistical properties. The motivation for the model comes from the growth of several kinds of real networks (i.e., kinship and trading networks, networks of corporate alliances, networks of autocatalytic chemical reactions). These networks grow either by establishing closer connections by adding links in the existing network or by adding new nodes. A node in these networks lacks the information of the entire network. In order to establish a closer connection to other nodes it starts a search in the neighboring part of the network and waits for a possible feedback from a distant node that received the "searching signal." Our model imitates this behavior by growing the network via the addition of a link that creates a cycle in the network or via the addition of a new node with a link to the network. The forming of a cycle creates feedback between the two ending nodes. After choosing a starting node, a search is made for another node at a suitable distance; if such a node is found, a link is established between this and the starting node, otherwise (such a node cannot be found) a new node is added and is linked to the starting node. We simulate this algorithm and find that we cannot reject the hypothesis that the empirical degree distribution is a q-exponential function, which has been used to model long-range processes in nonequilibrium statistical mechanics.
我们提出了一种网络形成模型，并研究了它的一些统计特性。该模型的动机来自于几种真实网络（即亲属关系和交易网络、企业联盟网络、自催化化学反应网络）的增长。这些网络要么通过在现有网络中添加链接来建立更紧密的连接，要么通过添加新节点来增长。这些网络中的一个节点缺乏整个网络的信息。为了与其他节点建立更紧密的连接，它开始在网络的相邻部分进行搜索，并等待来自接收到“搜索信号”的远程节点的可能反馈。我们的模型通过添加在网络中创建循环的链接或通过添加与网络有链接的新节点来增长网络，从而模仿这种行为。循环的形成在两个端点节点之间产生反馈。选择一个起始节点后，在合适的距离搜索另一个节点；如果找到这样一个节点，则在该节点与起始节点之间建立链接，否则（找不到这样的节点）添加一个新节点并将其链接到起始节点。我们模拟了这个算法，发现我们不能拒绝经验度分布是一个q指数函数的假设，该函数已被用于对非平衡统计力学中的长程过程进行建模。
