  Given a simple undirected graph $G$, the maximum $k$-club problem is to find
a maximum-cardinality subset of nodes inducing a subgraph of diameter at most
$k$ in $G$. This NP-hard generalization of clique, originally introduced to
model low diameter clusters in social networks, is of interest in network-based
data mining and clustering applications. We give two MAX-SAT formulations of
the problem and show that two exact methods resulting from our encodings
outperform significantly the state-of-the-art exact methods when evaluated both
on sparse and dense random graphs as well as on diverse real-life graphs from
the literature.
