The aim of this paper is to analyze the distribution of convenient position-values defined on a connected undirected graph. Such values are defined only by the connectiveity of the graph, but meet equilbrium condition on the graph. First, we prove the convenient position-value are distributed according to gravity model using a negative exponential distribution. Then, we exhibit the echo effect and characterize the distribution of convenient position-value on a monocentric city. Finally, we compare radial, external ring and radial-arc graphs routings in terms of convenient position-values.