Detecting Communities in Social Networks by Optimizing Similarity and Modularity Measures

INTRODUCTION
The most common means of contact nowadays are social networks. People can voice their opinions, disseminate information, advertise products and services, publicize upcoming events, connect with powerful individuals, and engage in political discourse. Hence, data on the social media platform is growing substantially. The data explosion has presented fresh obstacles to the visualization and analysis of social network data. Networks with community structure as a key characteristic are common, and social networks are a good illustration of this. Finding groups within networks is an important problem. Consequently, numerous approaches to community detection have been put out in the literature thus far [1]. The behavior of complicated networks can be better understood with the aid of community structure. Similar to communities, it is a set of linked online pages around a certain subject. Communities aid in marketing, information transmission, comprehension, analysis, discovering hidden patterns, recommendation systems, and location-based interaction analysis. An example of a subgraph in a network is a community, which is a group of nodes (individuals) that facilitates communication and the growth of interpersonal relationships. Different names for communities include modules, groups, and clusters. According to [2] the community structure is characterized by a collection of nodes that are more densely packed inside a group and less densely packed between other groups. This article introduces the “Cosine Shared Link Method (CSLM)” a novel technique that relies on cosine similarity. The foundation of CSLM is the cosine similarity measure and the agglomerative greedy technique. Analyzing real-world networks is possible using this technology, which is highly efficient.

Methodology
To identify communities in intricate networks, researchers have developed the Cosine Shared Link Method (CSLM) [3] a greedy agglomerative hierarchical approach. Starting from the ground up, CSLM uses a cosine similarity metric to repeatedly combine nodes into communities, and then uses modularity to assess the quality of these communities. There are three primary steps to the process:
Metric for Similarity: There is an initial assumption that each node is a separate community. The technique calculates the Cosine Shared Link Score (CSLS) for each node j and uses it to assess possible moves to each of its surrounding communities g,. With this score, we can see how closely node j is related to community g, by calculating the cosine similarity and the density of their common connections. Once node j finds a neighbor with the highest CSLS, it shifts to that neighbor. Once the community structure has stabilized, the process is repeated for all nodes.
Optimization of Modularity: Following the establishment of initial communities, the algorithm calculates the network’s modularity Q, a measure of the strength of the community structure, in order to optimize modularity. A function that determines the modularity is
where W is the weight of the link between nodes j and k_t d_j and d_k are the degrees of nodes j and k_r and l is the total number of connections in the network, individually. Reaching the most coherent community structure is the goal of the algorithm, which seeks to maximize Q.
Aggregation of Community: Here, the algorithm takes the communities it retrieved in the previous step and adds them together. The network is reorganized such that each node is now seen as belonging to a bigger community. The total link weights within each group are used to calculate the link weights among these aggregated communities. After then, the combined network goes through the same procedure again and again until the modularity value converges, which means the community structure is stable.
Using these processes in an iterative fashion, CSLM efficiently finds community structures in big networks, making use of the power of modularity optimization and cosine similarity measurements to guarantee accurate and coherent community detection.

Experiments and Results
The proposed “Cosine Shared Link Method (CSLM)” is tested on five real-world networks and compared with the PyLouvain and Louvain methods [4]. The evaluation criterion used is modularity [5]. Table 1.1 outlines the parameters used, and Table 1.2 provides descriptions of the datasets.

The Cosine Shared Link Method (CSLM) was tested against the PyLouvain and Louvain methods on five real-world networks (Football, Email, Facebook, Citations, and Brightkite). The comparison focused on modularity and community detection. CSLM consistently outperformed the other methods, achieving higher modularity values in most cases, as shown below in given tables and figures

Conclusion
Identifying communities in big, complicated networks is a problem that has received a lot of attention recently. The community structure of complicated systems can be revealed using a number of recently developed efficient methods. Research into the examination of communities within intricate networks has recently attracted a lot of attention. The unveiling group in complicated networks has been the subject of a plethora of proposed methodologies. To reveal communities in complicated networks, we have presented a method, the CSLM approach, which is based on the iterative agglomerative greedy strategy. In complicated networks, the CSLM approach maximizes the modularity value. The value of modularity indicates the caliber of the network community. For this network community detection task, we have employed a novel similarity metric, CSLS. CSLS is a hybrid of the cosine similarity metric and the shared link metric. When two nodes are similar, the CSLS will find them. After that, the nodes that have a high CSLS are paired with the node that is most comparable to them. Moreover, CSLM’s output is validated in actual networks. The CSLM achieves better results than the current methods for community detection. Finding partitions in big networks using the CSLM takes linear time. When compared to the current approaches, the modularity value produced with CSLM is significantly higher. This indicates that compared to other methods, the community structure produced by CSLM is of higher quality. The results of the trial validate the efficacy and precision of our method.
References

1. Morrison, M., & Gabbay, M. (2020). Community detectability and structural balance dynamics in signed networks. Physical Review E, 102(1), 012304.
2. Riolo, M. A., & Newman, M. (2020). Consistency of community structure in complex networks. Physical Review E, 101(5), 052306.
3. Chaudhary, L., & Singh, B. (2020). Community detection using maximizing modularity and similarity measures in social networks. In Smart Systems and IoT: Innovations in Computing: Proceeding of SSIC 2019 (pp. 197-206). Springer Singapore.
4. Zhang, J., Fei, J., Song, X., & Feng, J. (2021). An improved Louvain algorithm for community detection. Mathematical Problems in Engineering, 2021(1), 1485592.
5. Fang, Y., Huang, X., Qin, L., Zhang, Y., Zhang, W., Cheng, R., & Lin, X. (2020). A survey of community search over big graphs. The VLDB Journal, 29, 353-392.