标题： 将自我中心的时间邻域推广以探测时间网络中的空间相关性并推断其拓扑结构 显示英文标题

标题： Generalizing Egocentric Temporal Neighborhoods to probe for spatial correlations in temporal networks and infer their topology

摘要： 小团簇被认为是社交面对面互动时间网络的一些基本组成部分。 然而，之前考虑的小团簇要么仅限于少量的节点和边，要么不包括三角形，而三角形被认为对于理解社交系统的动态至关重要。 因此，我们引入了一类新的小团簇，它们包括这些三角形，不限制节点或边的数量，并且可以在任何时间网络中高效挖掘。 将这些小团簇称为以边为中心的小团簇，我们通过分析展示了它们如何涵盖[A. Longa, G. Cencetti, B. Lepri, and A. Passerini, An efficient procedure for mining egocentric temporal motifs, Data Mining and Knowledge Discovery 36, 355 (2022)]中的以自我为中心的时间邻域小团簇。 我们还通过最大熵原理在实证数据中确认了以边为中心的小团簇相对于以自我为中心的小团簇带来了相关信息。 然后，我们展示了如何在网络中挖掘以边为中心的小团簇，可以用来探测产生该网络的底层动态中的空间相关性。 我们推导出了实证社交面对面互动网络中以边为中心的小团簇分布的近似公式。 在本文的最后一部分，我们探讨了如何利用以边为中心的小团簇的统计信息来推断它们所采样的网络的完整拓扑结构。 这导致了数学发展的需求，我们在此以图铺砌理论的名称开始了这一发展。 显示英文摘要

摘要： Motifs are thought to be some fundamental components of social face-to-face interaction temporal networks. However, the motifs previously considered are either limited to a handful of nodes and edges, or do not include triangles, which are thought to be of critical relevance to understand the dynamics of social systems. Thus, we introduce a new class of motifs, that include these triangles, are not limited in their number of nodes or edges, and yet can be mined efficiently in any temporal network. Referring to these motifs as the edge-centered motifs, we show analytically how they subsume the Egocentric Temporal Neighborhoods motifs of [A. Longa, G. Cencetti, B. Lepri, and A. Passerini, An efficient procedure for mining egocentric temporal motifs, Data Mining and Knowledge Discovery 36, 355 (2022)]. We also confirm in empirical data that the edge-centered motifs bring relevant information with respect to the Egocentric motifs by using a principle of maximum entropy. Then, we show how mining for the edge-centered motifs in a network can be used to probe for spatial correlations in the underlying dynamics that have produced that network. We deduce an approximate formula for the distribution of the edge-centered motifs in empirical networks of social face-to-face interactions. In the last section of this paper, we explore how the statistics of the edge-centered motifs can be used to infer the complete topology of the network they were sampled from. This leads to the needs of mathematical development, that we inaugurate here under the name of graph tiling theory.