Graph compression is essential for storing and analyzing large-scale graphs such as web crawls, social networks, and code repositories. In this paper we discuss new compression techniques for the Rust implementation of the WebGraph framework [9]. We take inspiration from Zuckerli’s [13] extensions to the classical Boldi–Vigna (BV) differential graph compression scheme, and propose a scalable, parallelizable compressor. We also develop a hybrid Huffman coding implementation with programmable maximum codeword length which makes it possible to eliminate context modeling and achieve faster decoding times with similar compression effectiveness. We obtain compression ratios up to 15 π codes, which further improve compression and increase encoding and decoding speed. We validate our approach on graphs ranging from hundreds of thousands to over a billion nodes, including a Software Heritage archive with ≈ 50 billion nodes and ≈ 854 billion arcs. In particular, we show that, unlike Zuckerli, we can improve at the same time both the compression ratio and the random-access speed with respect to WebGraph.
Clustering graphs, where the number of triangles is a constant fraction of the number of paths of length 2, appear frequently in real-world networks. Recently Chung showed that general clustering graphs are surprisingly structured in that they admit a regularity lemma; every clustering graph can be decomposed into a bounded number of random-like parts. We show that the regularity partition for clustering graphs can be computed in time O(nM( (G))) where M(n) is the complexity of n× n matrix multiplication and (G) is the maximum degree of the graph. In particular, we show that it is possible to efficiently find subcommunities of a clustering graph which have robust clustering; even after removing many edges, the subcommunity has a large clustering coefficient. Our algorithm is parallelizable and can be implemented in NC^2 . As a consequence of the proof, we show that sparse clustering graphs are closely related to dense quasirandom graphs.
Motivated by applications in cybersecurity such as finding meaningful sequences of malware-related events buried inside large amounts of computer log data, we introduce the "planted path" problem and propose an algorithm to find fuzzy matchings between two trees. This algorithm can be used as a "building block" for more complicated workflows. We demonstrate usefulness of a few of such workflows in mining synthetically generated data as well as real-world ACME cybersecurity datasets.
The increasing availability of relational data has contributed to a growing reliance on network-based representations of complex systems. Over time, these models have evolved to capture more nuanced properties, such as the heterogeneity of relationships, leading to the concept of multilayer networks. However, the analysis and evaluation of methods for these structures is often hindered by the limited availability of large-scale empirical data. As a result, graph generators are commonly used as a workaround, albeit at the cost of introducing systematic biases. In this paper, we address the inverse-generator problem by inferring the configuration parameters of a multilayer network generator, mABCD, from a real-world system. Our goal is to identify parameter settings that enable the generator to produce synthetic networks that act as digital twins of the original structure. We propose a method for estimating matching configurations and for quantifying the associated error. Our results demonstrate that this task is non-trivial, as strong interdependencies between configuration parameters weaken independent estimation and instead favour a joint-prediction approach.
Network structure and its role in prediction are examined in competitive basketball at the team and player levels. Adversarial game outcome networks from the National Collegiate Athletic Association (NCAA) Division I women’s basketball from 2021 to 2024 are used to compute the common out-neighbor score and PageRank, which are combined into a low-key leader strength that identifies competitors’ influence through structural similarity despite relatively low centrality. This measure is related to changes in NCAA NET rankings by grouping teams into quantiles and comparing average rank changes across seasons for both previous-to-current and current-to-next transitions. Link prediction is then studied using node2vec embeddings across three interaction settings. For NCAA regular-season game networks, cosine similarity between team embeddings is used as a feature in a logistic regression model to predict March Madness matchups. For the Women’s National Basketball Association (WNBA) shot-blocking networks, future directed blocking interactions are predicted via logistic regression on concatenated source-target player embeddings. For WNBA passing networks, region embeddings learned from first-quarter passes are evaluated for their ability to predict subsequent passing connections. Across NCAA and WNBA settings, embedding-based models provide statistically significant evidence that higher-order network structure contains predictive signals for future interactions, while the passing experiment shows weaker predictive performance but yields interpretable similarity patterns consistent with passing feasibility.
