Autocorrelation properties of temporal networks governed by dynamic node variables

Harrison Hartle, Naoki Masuda
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Abstract

We study synthetic temporal networks whose evolution is determined by stochastically evolving node variables - synthetic analogues of, e.g., temporal proximity networks of mobile agents. We quantify the long-timescale correlations of these evolving networks by an autocorrelative measure of edge persistence. Several distinct patterns of autocorrelation arise, including power-law decay and exponential decay, depending on the choice of node-variable dynamics and connection probability function. Our methods are also applicable in wider contexts; our temporal network models are tractable mathematically and in simulation, and our long-term memory quantification is analytically tractable and straightforwardly computable from temporal network data.
受动态节点变量支配的时空网络的自相关特性
我们研究了由随机演化的节点变量决定其演化的合成时空网络--即移动代理的时空邻近性网络等的合成类似物。我们通过边缘持久性的自相关度量来量化这些演化网络的长时间尺度相关性。根据节点变量动力学和连接概率函数的选择,会出现几种不同的自相关模式,包括幂律衰减和指数衰减。我们的方法也适用于更广泛的场合;我们的时空网络模型在数学上和模拟上都是可行的,我们的长期记忆量化在分析上是可行的,并且可以直接从时空网络数据中计算出来。
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