  Visualization of the adjacency matrix enables us to capture macroscopic
features of a network when the matrix elements are aligned properly. Community
structure, a network consisting of several densely connected components, is a
particularly important feature, and the structure can be identified through the
adjacency matrix when it is close to a block-diagonal form. However, classical
ordering algorithms for matrices fail to align matrix elements such that the
community structure is visible. In this study, we propose an ordering algorithm
based on the maximum-likelihood estimate of the ordered random graph model. We
show that the proposed method allows us to more clearly identify community
structures than the existing ordering algorithms.
