基于边的时空多层网络Katz中心性

中文摘要 AI 辅助

Katz中心性是一种成熟的度量方法，通过求解线性系统来识别和排序复杂网络中最重要节点。近期工作已发展了针对时间（即随时间演化）网络的Katz中心性概念。其缺点在于网络结构的微小变化可能导致网络大部分区域的中心性发生剧烈变化。此外，网络科学界不成比例的努力集中在基于节点的量研究上，而基于边的度量则远未被充分探索。在本手稿中，我们引入了一种新颖的故障感知时间多层网络模型，用于计算空间网络的基于边Katz中心性。这类网络允许使用线图作为网络表示。我们使用块三角和块带状超邻接矩阵表示，将层间连接建模为低秩矩阵，这为更新或降级边赋予了空间受限的强调。这些边可代表例如实时基础设施监控应用中水管/燃气管道的破裂或街道网络的阻塞。我们分析了块矩阵逆在块对角线上方块中条目衰减的结构。这产生了两种截断方法，允许大幅降低计算运行时间，代价是引入受控的截断误差。在规模高达$2\cdot 10^8$的一系列真实世界时空网络上的数值实验展示了准确性和效率，运行时间提升高达679倍。

英文摘要

Katz centrality is a well-established measure to identify and rank the most important nodes in complex networks by means of a linear system solve. Recent works have developed notions of Katz centrality for temporal, i.e., time-evolving networks. Their drawback is that small changes in the network structure may drastically change centralities across large parts of the network. Moreover, an unproportional effort in the network science community has been devoted to the study of node-based quantities while edge-based measures are far less explored. In this manuscript, we introduce a novel failure-aware temporal multiplex network model for computing edge-based Katz centralities for spatial networks. This class of networks admits the use of the line graph as network representation. We use a block-triangular and -banded supra-adjacency matrix representation, modeling inter-layer connections as low-rank matrices, which assigns a spatially constrained emphasis on up- or downdated edges. These could represent, e.g., breakages of water/gas pipes or obstructions in street networks in real-time infrastructure monitoring applications. We analyze the structure of the of the block matrix inverse with respect to entry decay in the blocks above the block-diagonal. This gives rise to two truncation approaches that allow drastic computational runtime reductions at the cost of introducing a controlled truncation error. Numerical experiments on a range of real-world spatio-temporal networks of size up to $2\cdot 10^8$ illustrate accuracy and efficiency with runtime gains of up to a factor of $679$.

发表机构

• Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore（恩尼奥·德·乔治数学研究中心，比萨高等师范学院）
• Dipartimento di Matematica, Alma Mater Studiorum Università di Bologna（博洛尼亚大学阿尔玛·mater学者学院数学系）
• IMATI-CNR, Pavia（帕维亚CNR应用数学研究所）
• Chair of Scientific Computing, Technische Universität Chemnitz, Department of Mathematics（开姆尼茨工业大学计算科学教席，数学系）

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