Higher-Order Neighborhood Truss Decomposition.

$k$-truss model is a typical cohesive subgraph model and has been received considerable attention. However, the $k$-truss model lacks the ability to reveal fine-grained structure information of the graph. Motivated by this, in this paper, we propose a new model named ($k$,$\tau$)-truss that considers the higher-order neighborhood ($\tau$ hop) information of an edge. Based on the ($k$,$\tau$)-truss model, we study the higher-order neighborhood truss decomposition problem which computes the ($k$,$\tau$)-trusses for all possible $k$ values regarding a given $\tau$. To address this problem, we first propose a bottom-up decomposition algorithm to compute the ($k$,$\tau$)-truss in the increasing order of $k$ values. Based on the algorithm, we devise three optimization strategies to further improve the decomposition efficiency. We evaluate our proposed model and algorithms on real datasets, and the experimental results demonstrate the effectiveness of the ($k$,$\tau$)-truss model and the efficiency of our proposed algorithms.