In this paper, we introduce a new method to compute magnitude homology of general graphs. To each direct sum component of magnitude chain complexes, we assign a pair of simplicial complexes whose simplicial chain complex is isomorphic to it. First we states our main theorem specialized to trees, which gives another proof for the known fact that trees are diagonal. After that, we consider general graphs, which may have cycles. We also demonstrate some computation as an application.

中文翻译：

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图幅值同源性的几何方法

在本文中，我们介绍了一种计算一般图幅值同源性的新方法。对于量链复形的每个直和分量，我们分配一对单形复形与其同构的单形复形。首先，我们陈述专门针对树的主要定理，这为树是对角的这一已知事实提供了另一个证明。之后，我们考虑可能有环的一般图。我们还演示了一些计算作为应用程序。