Abstract
This paper analyses the rank of a path-link incidence matrix; that is, the number of independent link flows given all path flows. 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. We, therefore, discuss the rank of the matrix based on the flow conservation at each of the nodes. This study generally concludes that the rank is equal to the number of links minus the number of nodes exclusive of origin or destination nodes.
