A distance cartogram is a diagram that visualizes the proximity indices between points in a network, such as time-distances between cities. The Euclidean distances between the points on the distance cartogram represent the given proximity indices. This is a useful visualization tool for the level of service of transport, e.g. difference in the level of service between regions or points in a network and its improvement in the course of time. The two previously proposed methods—multidimensional scaling (MDS) and network time-space mapping—have certain advantages and disadvantages. However, we observe that these methods are essentially the same, and the merits of both these methods can be combined to formulate a generalized solution. In this study, we first formulate the time-space mapping problem, which includes the key features of both of the above stated methods, and propose a generalized solution. We then apply this solution to the time-distances of Japan's railway networks to confirm its applicability.