The spatial arrangement of cells within tissues plays a pivotal role in shaping tissue function. A critical spatial pattern is network motif as cell organization. Network motifs can be represented as recurring significant interconnections in a spatial cell-relation graph, i.e., the occurrences of isomorphic subgraphs in the graph, which is computationally infeasible to have an optimal solution with high-order (>3 nodes) subgraphs. We introduce Triangulation Network Motif Neural Network (TrimNN), a neural network-based approach designed to estimate the prevalence of network motifs of any order in a triangulated cell graph. TrimNN simplifies the intricate task of occurrence regression by decomposing it into several binary present/absent predictions on small graphs. TrimNN is trained using representative pairs of predefined subgraphs and triangulated cell graphs to estimate overrepresented network motifs. On typical spatial omics samples within thousands of cells in dozens of cell types, TrimNN robustly infers high-order network motifs in seconds. TrimNN provides an accurate, efficient, and robust approach for quantifying network motifs, which helps pave the way to disclose the biological mechanisms underlying cell organization in multicellular differentiation, development, and disease progression.