  We analyze the impact of transient and Byzantine faults on the construction
of a maximal independent set in a general network. We adapt the
self-stabilizing algorithm presented by Turau \cite{turau2007linear} for
computing such a vertex set. Our algorithm is self-stabilizing and also works
under the more difficult context of arbitrary Byzantine faults.
  Byzantine nodes can prevent nodes close to them from taking part in the
independent set for an arbitrarily long time. We give boundaries to their
impact by focusing on the set of all nodes excluding nodes at distance 1 or
less of Byzantine nodes, and excluding some of the nodes at distance 2. As far
as we know, we present the first algorithm tolerating both transient and
Byzantine faults under the fair distributed daemon. We prove that this
algorithm converges in $ \mathcal O(\Delta n)$ rounds w.h.p., where $n$ and
$\Delta$ are the size and the maximum degree of the network, resp.
Additionally, we present a modified version of this algorithm for anonymous
systems under the adversarial distributed daemon that converges in
  $ \mathcal O(n^{2})$ expected number of steps.
