Multi-View Structural Graph Summaries (2407.18036v2)

Abstract: A structural graph summary is a small graph representation that preserves structural information necessary for a given task. The summary is used instead of the original graph to complete the task faster. We introduce multi-view structural graph summaries and propose an algorithm for merging two summaries. We conduct a theoretical analysis of our algorithm. We run experiments on three datasets, contributing two new ones. The datasets are of different domains (web graph, source code, and news) and sizes; the interpretation of multi-view depends on the domain and are pay-level domains on the web, control vs.\@ data flow of the code, and news broadcasters. We experiment with three graph summary models: attribute collection, class collection, and their combination. We observe that merging two structural summaries has an upper bound of quadratic complexity; but under reasonable assumptions, it has linear-time worst-case complexity. The running time of merging has a strong linear correlation with the number of edges in the two summaries. Therefore, the experiments support the assumption that the upper bound of quadratic complexity is not tight and that linear complexity is possible. Furthermore, our experiments show that always merging the two smallest summaries by the number of edges is the most efficient strategy for merging multiple structural summaries.

• The paper introduces multi-view graph summarization using distinct models (AC, CC, and ACC) to create concise structural representations.
• It develops an innovative merging algorithm that overcomes redundancy challenges and achieves near-linear runtime under practical conditions.
• Empirical evaluations on diverse datasets validate the method’s efficiency and robustness, highlighting its impact on large-scale graph processing.

An Expert Overview of "Multi-View Structural Graph Summaries"

The paper "Multi-View Structural Graph Summaries" introduces a novel approach for efficiently summarizing graph structures by employing multi-view capabilities. The authors focus on creating concise representations, called structural graph summaries, which are essential for reducing computational overhead in tasks that involve large graph datasets. A key contribution of this work is the development of an algorithm for merging multiple graph summaries, enabling faster processing compared to working with the full original graphs.

Research Contributions

1. Multi-View Graph Summarization:
   • The authors explore the conceptualization of multi-view graphs as several representations of a base graph, emerging from either differing domain interpretations or various source depictions. This multi-view notion is concretized through real-world datasets spanning diverse domains such as web graphs, source code, and news articles.
   • The paper details the creation of graph summaries using three models—attribute collection (AC), class collection (CC), and their combination (ACC)—tailored to distinct application needs.
2. Merging Algorithm for Summaries:
   • A central algorithm is developed for merging two graph summaries, overcoming challenges like redundancy and inconsistencies that arise in naive unions. This method adapts well across different graph summary types, handling cases of overlapping and distinct structural schema.
   • The algorithm not only theoretically caps merging complexity to quadratic behavior but is empirically shown to achieve near-linear complexity under practical assumptions, facilitated by leveraging efficient data structuring and access strategies.
3. Empirical Evaluation:
   • The merging process is tested on datasets of varying scale and origin, including the Billion Triple Challenge 2019, R-source code abstracts, and news data synthesized using GPT-4. The results demonstrate the robustness and efficiency of the algorithm, with merging strategies optimizing runtime performance.
   • Different strategies for multi-summary merging are compared, such as smallest- and largest-first, with findings indicating that merging smaller summaries first often provides optimal speed.

Implications and Future Directions

This paper's contributions have significant theoretical and practical implications for data processing in graph databases and networks. The multi-view graph summary provides nuanced insights into complex data ecosystems by capturing different perspectives of the underlying data. From a theoretical standpoint, the proposed methods challenge prevailing assumptions about the upper bounds of graph operations, suggesting potential improvements in real-time data handling and processing.

Looking ahead, the integration of more sophisticated payloads or enhanced categorical distinctions in EQCs (Equivalence Classes) might enrich the structural fidelity of graph summaries. Further exploration of multi-hop summary models could unravel new dimensions of graph theory applications, particularly in machine learning contexts where graph embeddings play a critical role in prediction accuracy.

The methodological innovations set forth by this research can act as a catalyst for future work in efficient data summarization, affecting fields as diverse as semantic web analysis, large-scale data management, and algorithmic data science.