# An Edge-Based Approach to Partitioning and Overlapping Graph Clustering with User-Specified Density
## 4 Proposed Partitioning and Overlapping Clustering Method
### Overlapping Clustering
The identification of clusters in a complex network with closely matched density holds strategic advantages as resource allocation can be completed effectively across all clusters. This not only streamlines the deployment of resources but also enhances the efficiency of cluster monitoring. The overlapping areas within the context of overlapping clustering introduce a dimension of particular interest. Allocating resources to nodes within these areas enables coverage across multiple clusters; this provides both resource optimization and identification of regions that may require special attention. In practical terms, users can interpret and select density values based on the specific requirements of their application. For instance, in the context of monitoring the spread of infectious diseases, such as COVID-19, overlapping areas identified by the clustering may indicate potential superspreader locations, emphasizing the algorithm's relevance in this domain. Awareness of the user-specified density range and network topologies is imperative for users, significantly influencing the precise density specification and the ensuing effectiveness of clustering outcomes in specific applications. The proposed algorithm represents a significant advancement in the realm of graph clustering. In contrast to traditional approaches, the algorithm introduces a novel perspective by prioritizing clustering based on user-required density. This is also valuable in understanding of network structures. Furthermore, the algorithm's capability to identify clusters with user-specified density values contributes to its practical applicability in real-world settings. This feature not only sets the proposed algorithm apart from the existing literature but also extends its potential to address the inherent shortcomings of conventional graph clustering methods. ## 9 Future Directions

Future work can be carried out from several aspects. The following merit further study. They are, by no means, a comprehensive list of all possible directions. * Graph clustering type: This work proposed an approach for both partitioning and overlapping graph clustering. Hierarchical graph clustering is a natural extension. In practice, their applications may be relatively fewer. However, the recent drone communication network is a prime example as they are naturally formed in the hierarchy in some applications. Both agglomerative and divisive approaches in hierarchical clustering can be studied. The critical issues are the suitable level of hierarchy (if they do not initially exist) and whether partitioning or overlapping or both types of clustering are allowed at each level. The objectives of the application are likely to dictate the direction of investigation. * Sensitivity analysis: The approach is initiated for an edge with an average degree. In some cases, there may be more than one of such edge. This work considers them equally and selects any one to initiate clustering. In such cases, it may be worth investigating the impact of different starting edges on the resultant clusters and their MRDCC values. * Incorporation of edge centralities: Different kinds of edge centralities exist and some are already utilized in graph clustering algorithms, especially in selecting the appropriate edge to split the graph. In situations with more than one edge with the average degree, different kinds of edge centralities may be applied to aid the selection. This may result in better clustering performances. * A more complex form of a graph: Graph clustering in this work is the simplest kind (i.e., undirected unweighted graph). The complex form is the directed weighted graph; transportation problems are relevant examples. However, a directed unweighted graph may be a good candidate for the next stage. Many bioinformatics datasets are qualified for such studies. Alternatively, undirected weighted can also be studied, where weights may represent frequency during communication of two sources.