###### Abstract  
This study addresses the importance of focal nodes in understanding the structural composition of networks. To identify these crucial nodes, a novel technique based on parallel Fuzzy Cognitive Maps (FCMs) is proposed. By utilising the focal nodes produced by the parallel FCMs, the algorithm efficiently creates initial clusters within the population. The community discovery process is accelerated through a distributed genetic algorithm that leverages the focal nodes obtained from the parallel FCM. This approach mitigates the randomness of the algorithm, addressing the limitations of the random population selection commonly found in genetic algorithms. The proposed algorithm improves the performance of the genetic algorithm by enabling informed decision making and forming a better initial population. This enhancement leads to improved convergence and overall algorithm performance. Furthermore, as graph sizes grow, traditional algorithms struggle to handle the increased complexity. To address this challenge, distributed algorithms are necessary for effectively managing larger data sizes and complexity. The proposed method is evaluated on diverse benchmark networks, encompassing both weighted and unweighted networks. The results demonstrate the superior scalability and performance of the proposed approach compared to the existing state-of-the-art methods.  
parallel fuzzy cognitive maps; distributed genetic algorithm; community detection; focal nodes; social networks +
Footnote †: journal: Applied  
0000-0001-9993-3300-3300-3300-3300-3300-3300-3300-3300-33  
focal nodes in the graphs becomes increasingly difficult as the size and complexity of the graphs increase. This paper explores the possibility of using a fuzzy-cognitive-map-based approach to identify the focal nodes in a given network. The fuzzy cognitive map is a system motivated by the human capability of reasoning. It embodies a perception-based system. It uses an iterative learning method to acquire knowledge about a particular system and to determine the system's various attributes. One of the largest impediments to utilising FCM for complicated systems is the difficulty of the algorithm in handling huge datasets. The suggested study tackles this specific issue and discusses a parallel fuzzy cognitive map method. When a genetic algorithm is employed to detect the community structure of the network, there is a quotient of randomness associated with the initial population selection. The focal nodes identified are then used to detect the community structure in the network thus reducing the randomness of the genetic algorithm. Following that, a distributed genetic algorithm is employed to detect the network's communities.  
The key contributions of this research study can be summarised as follows:  
* A parallel fuzzy cognitive map is used for the identification of focal nodes, which reduces the time complexity of the problem;
* A novel distributed approach for community detection using a genetic algorithm is proposed;
* To accelerate the convergence of the genetic algorithm, the focal nodes of the network are provided as input, thus reducing the randomness of the initial population.  
The paper is organized as follows. In Section 2, recent works in fuzzy cognitive maps and the use of genetic algorithms for community detection are discussed. In Section 3, a detailed elucidation of the proposed methods is given. Section 4 elaborates on the experimental framework used. In Section 5, the results obtained are compared and analysed while in Section 6, conclusions are provided.