Entropy of network ensembles
Entropy of network ensembles
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DOI：
10.1103/physreve.79.036114
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发表时间：
2009-03-01
影响因子：
2.4
通讯作者：
Bianconi, Ginestra
中科院分区：
文献类型：
--
作者：
Bianconi, Ginestra
本文推广随机网络的概念，用统计力学的方法来描述具有非平凡特征的网络系综。该框架能够描述无向和有向网络集成以及加权网络集成。这些网络可能具有重要的社区结构，或者，在嵌入给定空间的网络的情况下，它们可能具有与节点之间的距离有重要依赖关系的链接概率。这些集成由它们的熵来表征，熵用来评估集成中网络的基数。特别地，本文定义并评价了结构熵，即具有给定度序列的无向不相关简单网络系综的熵。我们强调一个明显的悖论，即无标度分布的特点是具有小的结构熵，而它们在自然、社会和技术复杂系统中如此广泛地遇到。我们通过证明无标度分布是具有相应结构熵值的最可能的度分布，提出了一个解决这个悖论的方法。最后，我们在本文中提出的一般框架能够描述网络的微规范集成以及规范或隐变量网络集成，这对网络构建算法的制定具有重要意义。
In this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach. This framework is able to describe undirected and directed network ensembles as well as weighted network ensembles. These networks might have nontrivial community structure or, in the case of networks embedded in a given space, they might have a link probability with a nontrivial dependence on the distance between the nodes. These ensembles are characterized by their entropy, which evaluates the cardinality of networks in the ensemble. In particular, in this paper we define and evaluate the structural entropy, i.e., the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence. We stress the apparent paradox that scale-free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural, social, and technological complex systems. We propose a solution to the paradox by proving that scale-free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy. Finally, the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden-variable network ensembles with significant implications for the formulation of network-constructing algorithms.