"Iterative approximate Byzantine consensus in arbitrary directed graphs"

We explore the problem of Iterative approximate consensus in the presence of Byzantine adversaries. The problem has been studied in complete graph, but to our best knowledge, the problem in arbitrary graph in point-to-point network is still open. Inspired by the work in Iterative algorithm without faulty nodes, we prove the sufficient and necessary condition in this work. Moreover, we use our condition to examine whether such algorithm exists in some network, such as hypercube and Chord.