A theoretical study of the complexity of complex networks

The complexity of a network is an effective tool to analyze its structure. It predicts its performance and its reliability. In this paper, we evaluate the complexity of two complex networks: The Flower network and the Mosaic network. First, we propose two combinatorial approaches: the bipartition and the reduction that facilitate the calculation of the complexity of complex and large networks. Then, we combine these approaches in order to reveal the mechanism of the construction of our networks. We study their topological properties and we enumerate their spanning trees. Our results highlight the potential of our combinatorial approaches, which allow us to assess the complexity for two types of large and complex networks as the Flower network and the Mosaic network.