人与人面对面交互时间网络中的因果路径
Causal Paths in Temporal Networks of Face-to-Face Human Interactions
摘要：
在时间网络中，因果路径的特征在于从源到目标的链接必须遵守时间顺序。在这篇文章中，我们研究了在不同的社会背景下，人类面对面互动的时间网络中的因果路径结构。在静态网络中，路径是可传递的，即从$a$到$b$以及从$b$到$c$的链路的存在意味着从$a$经由$b$到$c$的路径的存在。在时间网络中，时序约束引入了影响传递性的时间相关性。一个基于高阶马尔可夫链的概率模型表明，只有当连续事件之间的时间间隔大于平均值时，才存在使传递性失效的相关性，并且在低于该值时可以忽略不计。时间和静态可达性矩阵的密度之间的比较表明，静态表示可以使用良好的近似。此外，我们量化的因果连接区域的网络随着时间的推移的程度。
英文摘要：
In a temporal network causal paths are characterized by the fact that links from a source to a target must respect the chronological order. In this article we study the causal paths structure in temporal networks of human face to face interactions in different social contexts. In a static network paths are transitive i.e. the existence of a link from $a$ to $b$ and from $b$ to $c$ implies the existence of a path from $a$ to $c$ via $b$. In a temporal network the chronological constraint introduces time correlations that affects transitivity. A probabilistic model based on higher order Markov chains shows that correlations that can invalidate transitivity are present only when the time gap between consecutive events is larger than the average value and are negligible below such a value. The comparison between the densities of the temporal and static accessibility matrices shows that the static representation can be used with good approximation. Moreover, we quantify the extent of the causally connected region of the networks over time.
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