  Anti-rumor dynamics is proposed on the basis of rumor dynamics and the
characteristics of anti-rumor dynamics are explored by both mean-field
equations and numerical simulations on complex network. The main metrics we
study are the timing effect of combating rumor and the identification of
influential nodes, which are what an efficient strategy against rumor may
concern about. The results indicate that, there exists robust time dependence
of anti-rumor dynamics and the timing threshold emerges as a consequence of
launching the anti-rumor at different delay time after the beginning of rumor
spreading. The timing threshold as a critical feature is further verified on a
series of Barabasi-Albert scale-free networks (BA networks), where anti-rumor
dynamics arises explicitly. The timing threshold is a network-dependent
quantity and its value decreases as the average degree of the BA network
increases until close to zero. Meanwhile, coreness also constitutes a better
topological descriptor to identify hubs. Our results will hopefully be useful
for the understanding of spreading behaviors of rumor and anti-rumor and
suggest a possible avenue for further study of interplays of multiple pieces of
information on complex network.
