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Note that this follows directly both from the deGroot theorem and from the opinion diffusion theorem above. However, we can go further and obtain a characterization result. An influence graph guarantees convergence of BDPs on it if and only if it contains no cycle other than self-loops:  \begin{theorem} \begin{proposition}  Let $\G$ be an influence profile. Then the following are equivalent:  \begin{itemize}  \item[] The BDP converges for any opinion profile $\O$ on $\G$.  \item [] $G$ contains no cycle of length $\leq 1$.  \end{theorem}  \en{proposition} \end{itemize}  \end{proposition}