Avena-Koenigsberger Andrea, Goñi Joaquín, Solé Ricard, Sporns Olaf
Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405-7007, USA.
Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405-7007, USA Indiana University Network Science Institute, Indiana University, Bloomington, IN 47405, USA.
J R Soc Interface. 2015 Feb 6;12(103). doi: 10.1098/rsif.2014.0881.
The structure of complex networks has attracted much attention in recent years. It has been noted that many real-world examples of networked systems share a set of common architectural features. This raises important questions about their origin, for example whether such network attributes reflect common design principles or constraints imposed by selectional forces that have shaped the evolution of network topology. Is it possible to place the many patterns and forms of complex networks into a common space that reveals their relations, and what are the main rules and driving forces that determine which positions in such a space are occupied by systems that have actually evolved? We suggest that these questions can be addressed by combining concepts from two currently relatively unconnected fields. One is theoretical morphology, which has conceptualized the relations between morphological traits defined by mathematical models of biological form. The second is network science, which provides numerous quantitative tools to measure and classify different patterns of local and global network architecture across disparate types of systems. Here, we explore a new theoretical concept that lies at the intersection between both fields, the 'network morphospace'. Defined by axes that represent specific network traits, each point within such a space represents a location occupied by networks that share a set of common 'morphological' characteristics related to aspects of their connectivity. Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.
近年来，复杂网络的结构备受关注。人们注意到，许多网络系统的现实世界例子都具有一系列共同的架构特征。这就引发了关于它们起源的重要问题，例如，这些网络属性是否反映了共同的设计原则，或者是否反映了塑造网络拓扑结构演化的选择力所施加的限制。是否有可能将复杂网络的众多模式和形式置于一个能揭示它们之间关系的共同空间中，以及决定实际演化出的系统在这样一个空间中占据哪些位置的主要规则和驱动力是什么？我们认为，可以通过结合两个目前相对不相关领域的概念来解决这些问题。一个是理论形态学，它已将由生物形态数学模型定义的形态特征之间的关系概念化。另一个是网络科学，它提供了众多定量工具来测量和分类不同类型系统中局部和全局网络架构的不同模式。在此，我们探索一个处于这两个领域交叉点的新理论概念——“网络形态空间”。由代表特定网络特征的轴所定义，这样一个空间内的每个点都代表着由具有一组与其连通性方面相关的共同“形态学”特征的网络所占据的位置。绘制网络形态空间揭示了现有网络填充该空间的程度，从而能够区分实际设计和不可能的设计，并突出贯穿复杂系统演化的规则和约束的生成潜力。
