The participation coefficient is a widely used metric of the diversity of a node's connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here as participation entropy, has been introduced as the Shannon entropy of the distribution of module labels across a node's connected neighbors. While diversity metrics have been studied theoretically in other literatures, including to index species diversity in ecology, many of these results have not previously been applied to networks. Here we show that the participation coefficient is a first-order approximation to participation entropy and use the desirable additive properties of entropy to develop new metrics of connection diversity with respect to multiple labelings of nodes in a network, as joint and conditional participation entropies. The information-theoretic formalism developed here allows new and more subtle types of nodal connection patterns in complex networks to be studied.

翻译：参与系数是衡量节点连接多样性的广泛使用指标，该多样性针对网络的模块划分。一种基于信息论的连接多样性概念（此处称为参与熵）已被引入，其定义为节点相连邻居的模块标签分布的香农熵。尽管多样性指标已在其他文献中进行了理论研究（包括生态学中物种多样性的指数化），但其中许多结果此前尚未应用于网络。本文证明参与系数是参与熵的一阶近似，并利用熵的期望可加性，以联合参与熵和条件参与熵的形式，开发了针对网络中节点多重标记的连接多样性新指标。本文发展的信息论形式体系使得研究复杂网络中节点连接模式的新颖且更微妙的类型成为可能。