  Current graph clustering methods emphasize individual node and edge con
nections, while ignoring higher-order organization at the level of motif. Re
cently, higher-order graph clustering approaches have been designed by motif
based hypergraphs. However, these approaches often suffer from hypergraph
fragmentation issue seriously, which degrades the clustering performance
greatly. Moreover, real-world graphs usually contain diverse motifs, with nodes
participating in multiple motifs. A key challenge is how to achieve precise
clustering results by integrating information from multiple motifs at the node
level. In this paper, we propose a multi-order graph clustering model (MOGC) to
integrate multiple higher-order structures and edge connections at node level.
MOGC employs an adaptive weight learning mechanism to au tomatically adjust the
contributions of different motifs for each node. This not only tackles
hypergraph fragmentation issue but enhances clustering accuracy. MOGC is
efficiently solved by an alternating minimization algo rithm. Experiments on
seven real-world datasets illustrate the effectiveness of MOGC.
