Analysis of higher-order organizations, usually small connected subgraphs
called motifs, is a fundamental task on complex networks. This paper studies a
new problem of testing higher-order clusterability: given query access to an
undirected graph, can we judge whether this graph can be partitioned into a few
clusters of highly-connected motifs? This problem is an extension of the former
work proposed by Czumaj et al. (STOC' 15), who recognized cluster structure on
graphs using the framework of property testing. In this paper, a good graph
cluster on high dimensions is first defined for higher-order clustering. Then,
query lower bound is given for testing whether this kind of good cluster
exists. Finally, an optimal sublinear-time algorithm is developed for testing
clusterability based on triangles