Abstarct: With core-periphery structure of networks based on edge density, core nodes are densely interconnected, peripheral nodes are connected to core nodes to different extents, and peripheral nodes are sparsely interconnected. Core-periphery structure composed of a single core and a single periphery has been observed for various networks. We propose scalable algorithms to detect multiple non-overlapping groups of core-periphery structure in a network. We also show that core-periphery structure with the configuration model (a standard random graph model that preserves the (expected) degree of each node) as the null model is possible only when we allow at least three blocks of nodes. Therefore, conventional core-periphery structure composed of a single block of core nodes and a single block of peripheral nodes is denied, because such a structure would have only two blocks. We illustrate our algorithms with model and empirical networks.