The induced path function J(u,v) of a graph consists of the set of all vertices lying on the induced paths between vertices u and v. This function is a special instance of a transit function. The function J satisfies betweenness if winJ(u,v) implies unotinJ(w,v) and xinJ(u,v) implies J(u,xsubseteqJ(u,v), and it is monotone if x,yinJ(u,v) implies J(x,y)subseteqJ(u,v). The induced path function of a
connected graph satisfying the betweenness and monotone axioms are characterized by transit axioms