This paper introduces a novel method for detecting community structure in complex networks based on extremal optimization of modularity. The method outperforms existing algorithms in terms of accuracy and efficiency. The algorithm uses a heuristic search inspired by the Extremal Optimization (EO) algorithm, which is related to natural optimization processes such as simulated annealing and genetic algorithms. The key idea is to optimize the modularity Q, which measures the quality of a community partition. The algorithm identifies the local variables contributing to Q and uses them to guide the optimization process. The method is tested on both simulated and real networks, including the Zachary karate club network, and shows superior performance compared to existing methods. The algorithm is able to detect communities even when they are more fuzzy, and it is efficient enough to handle large networks. The algorithm is also robust to different initializations and can escape local maxima. The results show that the algorithm achieves higher modularity values than previous methods, indicating a more accurate identification of community structure. The algorithm is applied to several real-world networks, including the jazz musicians network, university email network, C. elegans metabolic network, and author collaboration network. The results demonstrate the effectiveness of the algorithm in identifying community structure in complex networks. The paper concludes that the proposed method provides an accurate and efficient way to detect community structure in complex networks.This paper introduces a novel method for detecting community structure in complex networks based on extremal optimization of modularity. The method outperforms existing algorithms in terms of accuracy and efficiency. The algorithm uses a heuristic search inspired by the Extremal Optimization (EO) algorithm, which is related to natural optimization processes such as simulated annealing and genetic algorithms. The key idea is to optimize the modularity Q, which measures the quality of a community partition. The algorithm identifies the local variables contributing to Q and uses them to guide the optimization process. The method is tested on both simulated and real networks, including the Zachary karate club network, and shows superior performance compared to existing methods. The algorithm is able to detect communities even when they are more fuzzy, and it is efficient enough to handle large networks. The algorithm is also robust to different initializations and can escape local maxima. The results show that the algorithm achieves higher modularity values than previous methods, indicating a more accurate identification of community structure. The algorithm is applied to several real-world networks, including the jazz musicians network, university email network, C. elegans metabolic network, and author collaboration network. The results demonstrate the effectiveness of the algorithm in identifying community structure in complex networks. The paper concludes that the proposed method provides an accurate and efficient way to detect community structure in complex networks.