On the rank of a network incidence matrix

This paper analyses the rank of a path-link incidence matrix: that is, the number of independent link flows when all path flows are given. Although, in network analysis, the path-link incidence matrix is commonly used to define the structure of a transportation network, its fundamental properties have not been well studied. The authors therefore, discuss the rank of the matrix based on the flow conservation. This study generally concludes that the rank is equal to the number of nodes except the origin or destination nodes. [In Japanese.]