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high-order random walks
High-order random walks are stochastic graph traversal processes that model multi-step transition dynamics and multi-hop reachability to capture broader structural relationships beyond immediate neighborhood connections. Unlike standard first-order random walks that depend solely on direct transitions between adjacent nodes, high-order random walks incorporate longer sequence paths, powers of transition probability matrices, or higher-order relational structures such as network motifs and hypergraphs. By accumulating transition probabilities across extended paths, this approach models diffusion dynamics and structural similarities across a global topology. Consequently, high-order random walks enable network analysis and graph machine learning models to discover latent, long-range dependencies, distinguish meaningful affinities from local connectivity noise, and effectively characterize complex community structures.
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