We examine a node centrality measure based on the notion of total communicability, defined in terms of the row sums of the exponential of the adjacency matrix of the network. We argue that this is a natural metric for ranking nodes in a network, and we point out that it can be computed very rapidly even in the case of large networks. Furthermore, we propose the total sum of node communicabilities as a useful measure of network connectivity. Extensive numerical studies are conducted in order to compare this centrality measure with the closely related ones of subgraph centrality [E. Estrada and J. A. Rodriguez-Velazquez, Phys. Rev. E, 71 (2005), 056103] and Katz centrality [L. Katz, Psychometrica, 18 (1953), pp. 39-43]. Both synthetic and real-world networks are used in the computations.

M. Benzi

C. Klymko

Journal of Complex Networks

Journal of Complex Networks publishes original articles and reviews with a significant contribution to the analysis and understanding of complex networks and its applications in diverse fields. Complex networks are loosely defined as networks with nontrivial topology and dynamics, which appear as the skeletons of complex systems in the real-world. The journal covers everything from the basic mathematical, physical and computational principles needed for studying complex networks to their applications leading to predictive models in molecular, biological, ecological, informational, engineering, social, technological and other systems.     It includes, but is not limited to, the following topics:     - Mathematical and numerical analysis of networks   - Network theory and computer sciences   - Structural analysis of networks   - Dynamics on networks   - Physical models on networks   - Networks and epidemiology   - Social, socio-economic and political networks   - Ecological networks   - Technological and infrastructural networks   - Brain and tissue networks   - Biological and molecular networks   - Spatial networks   - Techno-social networks i.e. online social networks, social networking sites, social media   - Other applications of networks   - Evolving networks   - Multilayer networks   - Game theory on networks   - Biomedicine related networks   - Animal social networks   - Climate networks   - Cognitive, language and informational network

The Journal of Complex Networks publishes original articles and reviews that significantly contribute to the analysis and understanding of complex networks and their applications across diverse fields. Complex networks are broadly defined as networks with nontrivial topology and dynamics, which serve as the skeletons of complex systems in the real world. The journal covers everything from the fundamental mathematical, physical, and computational principles necessary for studying complex networks to their applications that lead to predictive models in molecular, biological, ecological, informational, engineering, social, technological, and other systems. It includes, but is not limited to, the following topics: - Mathematical and numerical analysis of networks - Network theory and computer sciences - Structural analysis of networks - Dynamics on networks - Physical models on networks - Networks and epidemiology - Social, socio-economic, and political networks - Ecological networks - Technological and infrastructural networks - Brain and tissue networks - Biological and molecular networks - Spatial networks - Techno-social networks, i.e., online social networks, social networking sites, social media - Other applications of networks - Evolving networks - Multilayer networks - Game theory on networks - Biomedicine-related networks - Animal social networks - Climate networks - Cognitive, language, and informational networks.

《Journal of Complex Networks》期刊发表对复杂网络及其在各个领域应用的分析与理解有重要贡献的原创文章和综述。复杂网络被宽泛定义为具有非平凡拓扑和动态的网络，这些网络在现实世界中作为复杂系统的骨架。期刊涵盖了从研究复杂网络所需的基本数学、物理和计算原理，到其在分子、生物、生态、信息、工程、社会、技术等系统中应用的预测模型。具体包括但不限于以下主题：- 网络的数学和数值分析 - 网络理论与计算机科学 - 网络的结构分析 - 网络上的动态 - 网络的物理模型 - 网络与流行病学 - 社会、社会经济和政治网络 - 生态网络 - 技术和基础设施网络 - 大脑和组织网络 - 生物和分子网络 - 空间网络 - 技术社会网络（如在线社交网络、社交媒体） - 网络的其他应用 - 发展中的网络 - 多层网络 - 网络上的博弈论 - 生物医学相关网络 - 动物社会网络 - 气候网络 - 认知、语言和信息网络

Category	Quartile
数学	4
数学, 数学跨学科应用	4

Total communicability as a centrality measure

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Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	2