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 a class of outerplanar graphs and focus on the ranks of the groups along the main diagonal of magnitude homology.

幅值同源性是Hepworth和Willerton定义的有限图的大同性理论，它把由Leinster引入的被称为幅值的幂级数不变性分类。我们分析了幅度同源性中扭转的结构和含义。我们表明，任何有限生成的阿贝尔群都可以作为图的幅值同源性的一个子组出现，特别是，给定素数阶的扭转可以出现在图的幅值同源性中，并且有无数个这样的图。最后，我们提供了一类外平面图的幅值同源性的完整计算，并着眼于沿幅值同源性的主要对角线的组的秩。