  Network community detection is a hot research topic in network analysis.
Although many methods have been proposed for community detection, most of them
only take into consideration the lower-order structure of the network at the
level of individual nodes and edges. Thus, they fail to capture the
higher-order characteristics at the level of small dense subgraph patterns,
e.g., motifs. Recently, some higher-order methods have been developed but they
typically focus on the motif-based hypergraph which is assumed to be a
connected graph. However, such assumption cannot be ensured in some real-world
networks. In particular, the hypergraph may become fragmented. That is, it may
consist of a large number of connected components and isolated nodes, despite
the fact that the original network is a connected graph. Therefore, the
existing higher-order methods would suffer seriously from the above
fragmentation issue, since in these approaches, nodes without connection in
hypergraph can't be grouped together even if they belong to the same community.
To address the above fragmentation issue, we propose an Edge enhancement
approach for Motif-aware community detection (EdMot). The main idea is as
follows. Firstly, a motif-based hypergraph is constructed and the top K largest
connected components in the hypergraph are partitioned into modules.
Afterwards, the connectivity structure within each module is strengthened by
constructing an edge set to derive a clique from each module. Based on the new
edge set, the original connectivity structure of the input network is enhanced
to generate a rewired network, whereby the motif-based higher-order structure
is leveraged and the hypergraph fragmentation issue is well addressed. Finally,
the rewired network is partitioned to obtain the higher-order community
structure.
