图动力学的多面性
The Many Faces of Graph Dynamics
摘要：
复杂网络的拓扑结构已经吸引了研究人员几十年，导致了许多普遍性质的发现和不同类型的网络的重现特征。然而，今天对网络动力学的了解要少得多：事实上，复杂网络在现实中不是静态的，而是随着时间的推移而动态演变的。我们的论文的动机是经验观察，网络演化模式似乎远离随机，但表现出结构。此外，具体模式似乎取决于网络类型，与“一刀切”模式的存在相矛盾。然而，我们仍然缺乏量化这些直觉的可观测值，以及比较图演化的指标。这样的观测量和度量是外推或预测演化以及内插图演化所需要的。为了探索图动态的许多方面并量化时间变化，本文建议建立在中心性的概念上，这是一种衡量网络中节点重要性的方法。特别是，我们引入了中心距离的概念，两个图的自然相似性度量取决于一个给定的中心，表征图形类型。直观地说，中心性距离反映了两个图之间（非匿名）节点角色不同的程度，或者在动态图的情况下，随着时间的推移而变化。我们评估了五个进化模型和七个现实世界的社会和物理网络的中心距离方法。我们的研究结果经验表明，有用的中心距离表征图形动态相比，一个空模型的随机演化，并强调所考虑的方案之间的差异。有趣的是，我们的方法允许我们在规模和进化速度方面比较非常不同的网络的动态。
英文摘要：
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a "one fits it all" model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.
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