# An Edge-Based Approach to Partitioning and Overlapping Graph Clustering with User-Specified Density
## 2 Literature
Although the algorithm itself is parameter-free, graph clustering via modularity maximization may necessitate the adjustment of parameters like resolution, stopping criteria, and the modularity matrix computation method. The graph-based k-means algorithm is another parameter-free algorithm whereby minimum spanning trees are utilized to estimate k and centroid placement. Its proven high performance lies in handling noisy data [33]. Another noteworthy aspect of graph clustering includes Bayesian techniques. The Bayesian nonparametric methods have emerged as influential tools. These approaches provide a probabilistic framework for modeling complex relationships within graphs. Unlike traditional clustering methods that require a predetermined cluster count or some other parameters, Bayesian nonparametric techniques adaptively infer the number of clusters from the data. This flexibility is particularly advantageous in scenarios where the true number of clusters is unknown or varies. This makes Bayesian nonparametric methods well-suited for diverse real-world applications [34; 35]. Furthermore, these techniques inherently capture uncertainty in the clustering process, providing a probabilistic assignment of nodes to clusters. Models such as the Dirichlet Process Mixture Model (DPMM) [36; 37; 38; 39], Bayesian Community Detection (BCD) [40], Infinite Relational Model (IRM) [39; 40], and the Chinese Restaurant Process (CRP) fall under the Bayesian nonparametric umbrella and have found applications in diverse fields, including social network analysis, bioinformatics, and community detection in complex networks [41]. Despite the unprecedented flexibility and applicability of these techniques in diverse real-world scenarios, the effective clustering of graphs remains a significant area of exploration and refinement from several perspectives. An absence in the ability in specifying the required density of the resultant clusters is an avenue for research and improvement in this field. In the context of real networks characterized by intricately overlapping community structures, traditional methods prove insufficient for accurately identifying overlapped communities [42]. The existing approaches for identifying overlapped clusters can be broadly categorized into two main types. The first type includes node-based clustering algorithms (node clustering) that directly partition the network's nodes into distinct clusters by leveraging the available structural information. The second type are edge-based algorithms, where edges that typically have unique identities and edges that connect to a single node may belong to multiple link communities. These algorithms are referred to as 'edge' or 'link-based' clustering methods. However, it is worth noting that the majority of well-established algorithms predominantly fall within the first category. One notable approach that stands out is the Clique Percolation Method (CPM), which draws inspiration from clique percolation theory [43; 44]. It provides insights into the shared connections among nodes and enables the identification of multiple communities that overlap in terms of their node memberships. The Lancichinetti-Fortunato-Radicchi Measures (LFM) algorithm [45] detects overlapping and hierarchical community structures in complex networks by combining modularity and fitness optimization. This algorithm offers valuable insights into the complex nature of community structures. However, the LFM algorithm has limitations in handling large-scale networks due to its computational complexity. It also relies on predefined resolution parameters, which has an impact on its scalability and adaptability in real-world applications. The greedy clique expansion (GCE) algorithm, which was proposed in [46], is a strong way to find highly overlapping community structures in social networks by systematically expanding maximal cliques. GCE uncovers the intricate patterns of node overlaps and provides valuable insights into the complex relationships within communities.