## Abstract

Given an input graph G and a node v 2 G, homogeneous network embedding (HNE) maps the graph structure in the vicinity of v to a compact, fixed-dimensional feature vector. This paper focuses on HNE for massive graphs, e.g., with billions of edges. On this scale, most existing approaches fail, as they incur either prohibitively high costs, or severely compromised result utility. Our proposed solution, called Node-Reweighted PageRank (NRP), is based on a classic idea of deriving embedding vectors from pairwise personalized PageRank (PPR) values. Our contributions are twofold: first, we design a simple and efficient baseline HNE method based on PPR that is capable of handling billion-edge graphs on commodity hardware; second and more importantly, we identify an inherent drawback of vanilla PPR, and address it in our main proposal NRP. Specifically, PPR was designed for a very different purpose, i.e., ranking nodes in G based on their relative importance from a source node's perspective. In contrast, HNE aims to build node embeddings considering the whole graph. Consequently, node embeddings derived directly from PPR are of suboptimal utility. The proposed NRP approach overcomes the above efficiency through an effective and efficient node reweighting algorithm, which augments PPR values with node degree information, and iteratively adjusts embedding vectors accordingly. Overall, NRP takes O(mlog n) time and O(m) space to compute all node embeddings for a graph with m edges and n nodes. Our extensive experiments that compare NRP against 18 existing solutions over 7 real graphs demonstrate that NRP achieves higher result utility than all the solutions for link prediction, graph reconstruction and node classification, while being up to orders of magnitude faster. In particular, on a billion-edge Twitter graph, NRP terminates within 4 hours, using a single CPU core.

Original language | English |
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Pages (from-to) | 670-683 |

Number of pages | 14 |

Journal | Proceedings of the VLDB Endowment |

Volume | 13 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sept 2020 |

Event | 46th International Conference on Very Large Data Bases, VLDB 2020 - Virtual, Japan Duration: 31 Aug 2020 → 4 Sept 2020 |

## Scopus Subject Areas

- Computer Science (miscellaneous)
- Computer Science(all)