What are the relations between the edge weights and the topology in real-world graphs? Given only the topology of a graph, how can we assign realistic weights to its edges based on the relations? Several trials have been done for edge-weight prediction where some unknown edge weights are predicted with most edge weights known. There are also existing works on generating both topology and edge weights of weighted graphs. Differently, we are interested in generating edge weights that are realistic in a macroscopic scope, merely from the topology, which is unexplored and challenging. To this end, we explore and exploit the patterns involving edge weights and topology in real-world graphs. Specifically, we divide each graph into layers where each layer consists of the edges with weights at least a threshold. We observe consistent and surprising patterns appearing in multiple layers: the similarity between being adjacent and having high weights, and the nearly-linear growth of the fraction of edges having high weights with the number of common neighbors. We also observe a power-law pattern that connects the layers. Based on the observations, we propose PEAR, an algorithm assigning realistic edge weights to a given topology. The algorithm relies on only two parameters, preserves all the observed patterns, and produces more realistic weights than the baseline methods with more parameters.

翻译：真实世界中图结构的边权重与拓扑之间存在何种关系？仅依据图的拓扑结构，如何基于这些关系为其边分配合理的权重？已有研究尝试进行边权重预测，即在已知大部分边权重的情况下预测未知权重，同时存在同时生成加权图拓扑与边权重的相关工作。与此不同，我们关注的是仅从拓扑结构出发生成宏观层面现实合理的边权重——这一方向尚未被探索且颇具挑战性。为此，我们探究并利用真实世界图中边权重与拓扑的关联模式。具体而言，我们将每个图划分为若干层级，每个层级由权重不低于阈值的边构成。研究发现多个层级中呈现一致且惊人的模式：邻接性与高权重之间的相似性，以及高权重边占比随共同邻居数量近似线性增长的规律。此外还观察到连接不同层级的幂律分布模式。基于这些发现，我们提出PEAR算法，该算法仅需两个参数，即可为给定拓扑分配现实合理的边权重。与需要更多参数的传统基线方法相比，PEAR不仅能保留所有观测到的模式，还能生成更为真实的权重。