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Higher-Order Neighborhood Truss Decomposition

$k$-truss model is a typical cohesive subgraph model and has been received considerable attention recently. However, the $k$-truss model only considers the direct common neighbors of an edge, which restricts its ability to reveal fine-grained structure information of the graph. Motivated by this, in this paper, we propose a new model named $(k, τ)$-truss that considers the higher-order neighborhood ($τ$ hop) information of an edge. Based on the $(k, τ)$-truss model, we study the higher-order truss decomposition problem which computes the $(k, τ)$-trusses for all possible $k$ values regarding a given $τ$. Higher-order truss decomposition can be used in the applications such as community detection and search, hierarchical structure analysis, and graph visualization. To address this problem, we first propose a bottom-up decomposition paradigm in the increasing order of $k$ values to compute the corresponding $(k, τ)$-truss. Based on the bottom-up decomposition paradigm, we further devise three optimization strategies to reduce the unnecessary computation. We evaluate our proposed algorithms on real datasets and synthetic datasets, the experimental results demonstrate the efficiency, effectiveness and scalability of our proposed algorithms.