In transportation planning and network design, Braess paradox problem has been discussed for many decades. Those researches were originated from the simple network illustrated by Braess. Many works devoted to seek efficient methods to avoid the occurrence of paradox problem or find some rules for network designers to refer. Under arc-OD/path matrix is full column rank assumption i.e., the number of paths is less than the number of arcs plus origin/destination pairs, Dafermos and Nagurney derived the formulas to determine, whether Braess' paradox occurs in the network. In the large transportation networks, the number of path is larger than the number of arc, so their assumption is violated. The main purpose of this paper is to conquer the small network restriction. The generalized inverse method is used to relax the assumption presented by Dafermos and Nagurney.