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Social decisions made by individuals are easily influenced by information from their social neighborhoods. A key predictor of social contagion is the multiplicity of social contexts inside the individual's contact neighborhood, which is termed structural diversity. However, the existing models have limited decomposability for analyzing large-scale networks, and suffer from the inaccurate reflection of social context diversity. In this paper, we propose a new truss-based structural diversity model to overcome the weak decomposability. Based on this model, we study a novel problem of truss-based structural diversity search in a graph G, that is, to find the r vertices with the highest truss-based structural diversity and return their social contexts. o tackle this problem, we propose an online structural diversity search algorithm in $O(ρ(m+\mathcal{T}))$ time, where $ρ$, $m$, and $\mathcal{T}$ are respectively the arboricity, the number of edges, and the number of triangles in $G$. To improve the efficiency, we design an elegant and compact index, called TSD-index, for further expediting the search process. We further optimize the structure of TSD-index into a highly compressed GCT-index. Our GCT-index-based structural diversity search utilizes the global triangle information for fast index construction and finds answers in $O(m)$ time. Extensive experiments demonstrate the effectiveness and efficiency of our proposed model and algorithms, against state-of-the-art methods.