An efficient algorithm for the synthesis of fully consistent graphs

In this paper we present an efficient algorithm for the synthesis of fully consistent graphs. A consistent graph is a graph whose cyclic sum of edge weights along all loops is zero. It plays an important role in many sensor array processing applications like Time Difference of Arrival (TDOA) based source localization. By applying the concept of fundamental loops, a linearly independent basis of the loop space of the graph, our algorithm is able to find all consistent sets of edge weights for the full graph efficiently.