# GraphDBSCAN: Optimized DBSCAN for Noise-Resistant Community Detection in Graph Clustering
## 2 Related Works  
Community detection plays a crucial role in graph analysis, facilitating insights into social structures, biological networks, recommender systems, and citation networks. Various algorithms have been developed to uncover hidden community structures, broadly categorized into modularity-based, spectral, label propagation, and density-based clustering approaches. Each method exhibits distinct advantages and limitations in scalability, noise resilience, and parameter sensitivity. This section provides a detailed review of state-of-the-art community detection techniques and highlights their effectiveness in handling real-world and synthetic networks. Modularity-based community detection methods aim to maximize the modularity score, which evaluates how well communities are formed by comparing intra-community edge density to that of a random graph. Among the most widely used techniques in this category are Louvain [3,14] and Newman-Girvan [4,15]. Louvain Method: This algorithm employs a hierarchical clustering approach, iteratively merging smaller communities to maximize modularity. Louvain is particularly efficient for large-scale networks due to its greedy optimization strategy, making it significantly faster than spectral clustering or traditional hierarchical methods. However, a major drawback is the resolution limit problem, where small yet meaningful communities are merged into larger groups, leading to suboptimal clustering in some networks. Newman-Girvan Algorithm: This method uses edge betweenness centrality to iteratively remove the most influential edges, progressively splitting the network into distinct communities. While it provides interpretable hierarchical clustering, its computational complexity (O(n\({}^{3}\))) makes it unsuitable for large-scale graphs. Additionally, it tends to favor well-separated communities, making it less effective in highly interconnected networks. Other popular techniques include label propagation and spectral clustering, both of which take a different approach to community formation. Label Propagation Algorithm (LPA) [8,16]: This approach is computationally efficient and works by iteratively updating node labels based on their neighbors until convergence. One of its primary advantages is its scalability, as it does not require matrix computations, unlike spectral clustering. However, label propagation suffers from instability because it depends on the initial node labels, leading to inconsistent results across different runs. Additionally, in sparse networks, the label updates can lead to overly fragmented clusters that do not correspond to real-world communities. Spectral Clustering (SC) [4,17,18]: Spectral methods use eigenvalue decomposition of the graph Laplacian matrix to embed nodes into a low-dimensional space, where standard clustering methods such as k-means can be applied. This approach effectively captures global graph structure, making it more robust than purely local methods like modularity optimization. However, it requires predefining the number of communities, which is often unknown in real-world scenarios. Furthermore, its computational cost (O(n\({}^{3}\))) makes it infeasible for very large graphs, limiting its practical applicability. Beyond traditional approaches, alternative clustering techniques have emerged to address multi-dimensional and noisy data. For instance, unsupervised multi-view clustering methods, such as the fuzzy c-means algorithm proposed in [19], leverage multiple data perspectives to enhance clustering robustness. By incorporating fuzzy membership, this approach softens hard cluster assignments, offering flexibility in noisy or overlappingcommunities, though it struggles with scalability in large graphs. Similarly, weighted multi-view k-means clustering with L2 regularization [20] tackles multi-view data by assigning weights to views and regularizing the objective function, improving stability and noise resistance in high-dimensional settings.