We design efficient protocols for processors to extract private randomness over a network with Byzantine faults, when each processor has access to an independent weakly-random n-bit source of sufficient min-entropy.We give several such network extractor protocols in both the information theoretic and computational settings.For a computationally unbounded adversary, we construct protocols in both the synchronous and asynchronous settings.These network extractors imply efficient protocols for leader election (synchronous setting only) and Byzantine agreement which tolerate a linear fraction of faults,even when the min-entropy is only 2(log n) Omega(1).For larger min-entropy,in the synchronous setting the fraction of tolerable faults approaches the bounds in the perfect-randomness case.Our network extractors for a computationally bounded adversary work in the synchronous setting even when 99% of the parties are faulty, assuming trapdoor permutations exist. Further, assuming a strong variant of the Decisional Diffie-Hellman Assumption, we construct a network extractor in which all parties receive private randomness. This yields an efficient protocol for secure multi-party computation with imperfect randomness, when the number of parties is at least polylog (n) and where the parties only have access to an independent source with min-entropy nOmega(1).