# ADPSCAN: Structural Graph Clustering with Adaptive Density Peak Selection and Noise Re-Clustering
## 6 Conclusions  
In this paper, a novel structural graph clustering algorithm, ADPSCAN, is proposed, based on the adaptive selection of density peaks. To tackle the high dependency of traditional methods on external parameters, the generalized extreme value distribution is utilized to adaptively pinpoint potential clustering centers. Preliminary experiments have confirmed the validity of this method. Additionally, considering the potential misclassification of nodes as noise in existing algorithms, a distance-based structural similarity strategy has been devised. This strategy precisely measures the average distance scores between noise points and clusters, effectively reassigning noise nodes to their appropriate clusters. Comprehensive experiments on both real-world and synthetic network datasets demonstrate the effectiveness of the ADPSCAN algorithm. The results highlight its broad application potential in fields such as social network analysis, collaborative network research, and metabolic network functional module identification. Despite its robust performance, ADPSCAN's complexity is relatively high, with a worst-case time complexity of O(n\({}^{2}\)), where n represents the number of nodes in the network. This high complexity makes it unsuitable for ultra-large networks, such as the UK-2002 dataset from the Web Algorithmics Laboratory. The primary computational cost stems from calculating distance-based structural similarity. Future research could address scalability and speed issues by incorporating indexing and caching mechanisms, or by leveraging parallel computing and distributed systems.  
Conceptualization, X.D.; methodology, F.L.; software, X.D.; validation, X.D.; formal analysis, X.L.; investigation, F.L.; data curation, F.L.; writing--original draft preparation, X.D.; writing--review and editing, F.L.; visualization, X.D.; supervision, G.Y.; project administration, X.L.; All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: Data is contained within the article.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Karate**} & \multicolumn{2}{c}{**Polbooks**} & \multicolumn{2}{c}{**Dolphins**} & \\
**Algorithm** & **ARI\({}^{\star}\)** & **NMI\({}^{\star}\)** & **ARI\({}^{\star}\)** & **NMI\({}^{\star}\)** & **ARI\({}^{\star}\)** & **NMI\({}^{\star}\)** & **Avg.ARI\({}^{\star}\)** & **Avg.NMI\({}^{\star}\)** \\ \hline ADPSCAN & **1.000** & **1.000** & **0.668** & **0.601** & **0.935** & **0.889** & 0.868 & 0.845 \\ ADPSCAN- & 0.486 & 0.494 & 0.193 & 0.349 & 0.168 & 0.326 & 0.282 & 0.390 \\ \hline \hline \end{tabular} \({}^{\text{a}}\) ARI:AMeasures how similar two clustering results are, with values from \(-1\) to \(1\). Higher values mean more similarity. \({}^{\text{b}}\) NMI:Measures the shared information between two clustering results, with values from \(0\) to \(1\). Higher values mean better agreement. \({}^{\text{c}}\) Avg.ARI: Average Adjusted Rand Index across all datasets. \({}^{\text{d}}\) Avg.NMI: Average Normalized Mutual Information across all datasets. The bold values indicate the best performance for each dataset.  
\end{table}
Table 3: Ablation Study Results for Noise Re-clustering.