Complex networks, such as the World Wide Web (WWW), social networks, and biological networks, are found to be self-similar, contrary to previous beliefs that they are not. This study reveals that these networks exhibit self-similarity through a renormalization procedure that coarse-grains the network into boxes of a given size. The number of boxes needed to cover the network scales with the size of the box, indicating a self-similar structure. This self-similarity is characterized by a finite self-similar exponent, which is consistent across various networks, including the WWW, social networks, and protein-protein interaction networks. The results show that the scale-free property of these networks, where the degree distribution follows a power-law, is linked to their self-similar structure. The study also highlights the importance of considering the global structure of the network rather than local properties, as different methods of analysis can lead to different results. The findings suggest that complex networks, despite their diversity, share common self-organization dynamics that lead to a critical state. The results have implications for understanding the statistical physics of complex networks, fractals, and critical phenomena. The study also shows that the self-similarity of complex networks can be analyzed using the box covering method, which reveals the underlying scale-invariant properties of the network. The results are consistent across various networks, including the WWW, social networks, and biological networks, and provide a deeper understanding of the mechanisms that lead to the scale-free and self-similar properties of complex networks.Complex networks, such as the World Wide Web (WWW), social networks, and biological networks, are found to be self-similar, contrary to previous beliefs that they are not. This study reveals that these networks exhibit self-similarity through a renormalization procedure that coarse-grains the network into boxes of a given size. The number of boxes needed to cover the network scales with the size of the box, indicating a self-similar structure. This self-similarity is characterized by a finite self-similar exponent, which is consistent across various networks, including the WWW, social networks, and protein-protein interaction networks. The results show that the scale-free property of these networks, where the degree distribution follows a power-law, is linked to their self-similar structure. The study also highlights the importance of considering the global structure of the network rather than local properties, as different methods of analysis can lead to different results. The findings suggest that complex networks, despite their diversity, share common self-organization dynamics that lead to a critical state. The results have implications for understanding the statistical physics of complex networks, fractals, and critical phenomena. The study also shows that the self-similarity of complex networks can be analyzed using the box covering method, which reveals the underlying scale-invariant properties of the network. The results are consistent across various networks, including the WWW, social networks, and biological networks, and provide a deeper understanding of the mechanisms that lead to the scale-free and self-similar properties of complex networks.