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Abstract：
Understanding how different networks relate to each other is key for understanding complex systems. We introduce an intuitive yet powerful framework to disentangle different ways in which networks can be (dis)similar and complementary to each other. We decompose the shortest paths between nodes as uniquely contributed by one source network, or redundantly by either, or synergistically by both together. Our approach considers the networks\' full topology, providing insights at multiple levels of resolution: from global statistics to individual paths. Our framework is widely applicable across scientific domains, from public transport to brain networks. In humans and 124 other species, we demonstrate the prevalence of unique contributions by long-range white-matter fibers in structural brain networks. Across species, efficient communication also relies on significantly greater synergy between long-range and short-range fibers than expected by chance. Our framework could find applications for designing network systems or evaluating existing ones.
摘要：
了解不同网络之间的关系是理解复杂系统的关键。我们引入了一个直观而强大的框架，以解开网络可以彼此相似和互补的不同方式。我们分解由一个源网络唯一贡献的节点之间的最短路径，或者冗余地，或两者协同作用。我们的方法考虑了网络的完整拓扑，在多个分辨率级别提供见解：从全球统计到单个路径。我们的框架广泛适用于整个科学领域，从公共交通到大脑网络。在人类和其他124个物种中，我们证明了长程白质纤维在结构性脑网络中的独特贡献的普遍性.跨物种，有效的通信还依赖于远程和短程光纤之间比偶然预期的更大的协同作用。我们的框架可以找到用于设计网络系统或评估现有网络系统的应用程序。
