Since Hebb's postulate, many scientists, not only neuroscientists but also physicists and engineers, have paid much attention to the synaptic plasticity that called Hebb's learning rule because of its versatility. In particular, in the field of neuroscience, it is believed that his concept is important for the brain to realize its higher order functions: the development, learning and memory. Fifty years later from his postulate, it was found that the synaptic plasticity depends on the precise spike timing within tens of milliseconds between a pre- and postsynaptic neurons. This is called spike timing-dependent plasticity (STDP). It has been clarified that STDP induces the neuronal activities as observed in the cortex and hippocampus in the model study, but it is still unclear how these activities are induced. In order to understand it, it is essential to analyze structures, namely, how synaptic weights are organized on the recurrent networks. In this system, we observe that STDP organizes specific structures by analyses using complex network theory. In addition, these structures play important roles for neuronal activities in the networks.