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Intelligence needs connectivity and organization with some agents' intention in networks. The networks with intelligence produce some structure spontaneously. Therefore, it is important to focus on the structure in large networks like the Internet or World Wide Web that are constructed by human beings with their preferences or concepts. Especially, it has been found that even these artificial networks have scale-free structures, which are seen also in natural networks. It indicates that universal laws or phenomena exist in the properties and behaviors on scale-free networks. We investigate them from the view point of complex systems, in particular self-organization. From our proposed model and simulation experiments, it is found that growing scale-free networks have self-organized criticality. The phenomena would lead to the intelligence emerged from network structures.