  Magnitude homology is a bigraded homology theory for finite graphs defined by
Hepworth and Willerton, categorifying the power series invariant known as
magnitude which was introduced by Leinster. We analyze the structure and
implications of torsion in magnitude homology. We show that any finitely
generated abelian group may appear as a subgroup of the magnitude homology of a
graph, and, in particular, that torsion of a given prime order can appear in
the magnitude homology of a graph and that there are infinitely many such
graphs. Finally, we provide complete computations of magnitude homology of
outerplanar graphs and focus on the ranks of the groups along the main diagonal
of magnitude homology.
