Modelling the indirect cross-temporal relations in ranking dynamics via complex networks

Yitao Gao, Xiaomin Lyu, Bingsheng Chen and An Zeng

Chaos, Solitons & Fractals, 2026, vol. 209, issue P1

Abstract: Almost all real-world systems involve ranking. Previous studies have focused on super-stable nodes, ranking dynamics, and related phenomena. However, previous research treats ranking data merely as time series, which neglects the intrinsic indirect cross-temporal relations between time series. In this paper, we introduce the ranking network to explore the structural relationships underlying temporal ranking. This network modelling allows us to capture the indirect relation between nodes beyond their neighbours (i.e., indirect cross-temporal relations). By converting ranking series into a bipartite network of entities and ranks, we reveal consistent patterns: stability at extremes, fluctuation in the middle, and rank regression. Across time scales, ranking systems display long-range connections that generate structural distortions. Leveraging this framework, we propose a diffusion-based rank prediction method that surpasses traditional models using significantly less training data and shows particular strength during periods of large ranking shifts. The generality of our findings has been validated across multi-domain datasets.

Keywords: Ranking networks; Networked projection; Indirect cross-temporal interactions; Ranking prediction (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926005606

DOI: 10.1016/j.chaos.2026.118419

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