Graph Summarization (2004.14794v3)

Abstract: The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is graph summarization. It denotes a series of application-specific algorithms designed to transform graphs into more compact representations while preserving structural patterns, query answers, or specific property distributions. As this problem is common to several areas studying graph topologies, different approaches, such as clustering, compression, sampling, or influence detection, have been proposed, primarily based on statistical and optimization methods. The focus of our chapter is to pinpoint the main graph summarization methods, but especially to focus on the most recent approaches and novel research trends on this topic, not yet covered by previous surveys.

• The paper introduces a taxonomy classifying techniques into clustering, statistical, and goal-driven methods for effective graph summarization.
• It details various methodologies, including spectral clustering and graph convolutional networks, to condense and analyze complex graph data.
• Applications span query efficiency, visualization, and schema discovery, with future research directed at dynamic and heterogeneous graphs.

The paper "Graph Summarization" by Angela Bonifati, Stefania Dumbrava, and Haridimos Kondylakis provides an extensive overview of methodologies aimed at condensing graph data while preserving essential structural patterns and properties. Graph summarization serves multiple objectives: reducing data volume, enhancing query efficiency, facilitating visualization, and supporting analytics and cleaning.

Key Concepts in Graph Summarization

The authors begin by establishing foundational concepts of graph theory, defining undirected graphs (UG), directed graphs (DG), multi-graphs, attributed graphs (AG), knowledge graphs (KG), including geographical knowledge graphs (GG), and property graphs (PG). These concepts are crucial as different summarization techniques apply variably across graph types.

Recent Summarization Techniques

The paper explores various categories of graph summarization:

1. Graph Clustering: This is a significant focus categorized into structural and attributed-based methods. Structural clustering emphasizes graph topology, employing techniques like partitioning, spectral methods (e.g., Laplacian eigenmaps), and density-based methods to achieve noise-resistant clustering. Attributed clustering integrates feature attributes and applies network models like graph convolutional networks (GCNs) to represent and cluster nodes more effectively.
2. Statistical Summarization: This involves pattern-mining and sampling to reduce graphs. Techniques here focus on occurrence counting and pattern discovery, such as identifying geo-spatial biases in knowledge graphs for compact representation.
3. Goal-Driven Summarization: Methods in this category are tailored to optimize specific functions, such as memory footprint or relevance to queries, including handling dynamic or streaming graphs.

Key Findings and Taxonomy

A taxonomy is presented, classifying the summarization techniques based on their application: structural clustering, statistical methods, and goal-driven approaches. The taxonomy provides insights into the diverse applications and methodologies based on graph representations and summarization objectives.

Applications

Graph summarization has tangible applications in various domains:

• Query Efficiency: Summaries act as efficient indexes, accelerating query processing by reducing target data size.
• Visualization: Summaries provide a simpler view of complex graphs, making them more interpretable to end-users.
• Schema Discovery and Pattern Extraction: Summaries assist in identifying hidden patterns and potential schemas in data.

Future Research Directions

The paper pinpoints areas for future research, including:

• Developing methodologies for mixed datasets with numerical and categorical attributes.
• Designing incremental summary updates to manage dynamic graph evolutions.
• Establishing quality metrics and benchmarking processes for graph summaries.
• Extending graph summarization techniques to more expressive graph data models, like property graphs.

Overall, the paper serves as a comprehensive guide to contemporary graph summarization strategies, underscoring their relevance and utility in managing complex, large-scale graph data.