  Link prediction (LP), inferring the connectivity between nodes, is a
significant research area in graph data, where a link represents essential
information on relationships between nodes. Although graph neural network
(GNN)-based models have achieved high performance in LP, understanding why they
perform well is challenging because most comprise complex neural networks. We
employ persistent homology (PH), a topological data analysis method that helps
analyze the topological information of graphs, to explain the reasons for the
high performance. We propose a novel method that employs PH for LP (PHLP)
focusing on how the presence or absence of target links influences the overall
topology. The PHLP utilizes the angle hop subgraph and new node labeling called
degree double radius node labeling (Degree DRNL), distinguishing the
information of graphs better than DRNL. Using only a classifier, PHLP performs
similarly to state-of-the-art (SOTA) models on most benchmark datasets.
Incorporating the outputs calculated using PHLP into the existing GNN-based
SOTA models improves performance across all benchmark datasets. To the best of
our knowledge, PHLP is the first method of applying PH to LP without GNNs. The
proposed approach, employing PH while not relying on neural networks, enables
the identification of crucial factors for improving performance.
