Raimondo Sebastian, De Domenico Manlio
CoMuNe Lab, Center for Information and Communication Technology, Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo (TN), Italy and Department of Mathematics, University of Trento, Via Sommarive 9, 38123 Povo (TN), Italy.
CoMuNe Lab, Center for Information and Communication Technology, Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo (TN), Italy.
Phys Rev E. 2021 Feb;103(2-1):022311. doi: 10.1103/PhysRevE.103.022311.
Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. To compute the various topological descriptors commonly used to characterize the structure of a complex system (e.g., the degree, the clustering coefficient, etc.), it is usually necessary to completely reconstruct the network of relations between the subsystems. Several methods are available to detect the existence of interactions between the nodes of a network. By observing some physical quantities through time, the structural relationships are inferred using various discriminating statistics (e.g., correlations, mutual information, etc.). In this setting, the uncertainty about the existence of the edges is reflected in the uncertainty about the topological descriptors. In this study, we propose a methodological framework to evaluate this uncertainty, replacing the topological descriptors, even at the level of a single node, with appropriate probability distributions, eluding the reconstruction phase. Our theoretical framework agrees with the numerical experiments performed on a large set of synthetic and real-world networks. Our results provide a grounded framework for the analysis and the interpretation of widely used topological descriptors, such as degree centrality, clustering, and clusters, in scenarios in which the existence of network connectivity is statistically inferred or when the probabilities of existence π_{ij} of the edges are known. To this purpose, we also provide a simple and mathematically grounded process to transform the discriminating statistics into the probabilities π_{ij}.
从观测到的集体动力学中揭示复杂系统的结构特征是网络科学中的一个基本问题。为了计算通常用于表征复杂系统结构的各种拓扑描述符（例如，度、聚类系数等），通常需要完全重建子系统之间的关系网络。有几种方法可用于检测网络节点之间相互作用的存在。通过随时间观测一些物理量，使用各种判别统计量（例如，相关性、互信息等）来推断结构关系。在这种情况下，边存在的不确定性反映在拓扑描述符的不确定性中。在本研究中，我们提出了一个方法框架来评估这种不确定性，即使在单个节点的层面上，也用适当的概率分布取代拓扑描述符，从而避开重建阶段。我们的理论框架与在大量合成网络和真实世界网络上进行的数值实验一致。我们的结果为在通过统计推断网络连通性存在的场景中，或者当边的存在概率πij已知时，对广泛使用的拓扑描述符（如度中心性、聚类和簇）进行分析和解释提供了一个有根据的框架。为此，我们还提供了一个简单且有数学依据的过程，将判别统计量转换为概率πij。
