Summarization#
Graph summarization finds smaller representations of graphs resulting in faster runtime of algorithms, reduced storage needs, and noise reduction. Summarization has applications in areas such as visualization, pattern mining, clustering and community detection, and more. Core graph summarization techniques are grouping/aggregation, bitcompression, simplification/sparsification, and influence based. Graph summarization algorithms often produce either summary graphs in the form of supergraphs or sparsified graphs, or a list of independent structures. Supergraphs are the most common product, which consist of supernodes and original nodes and are connected by edges and superedges, which represent aggregate edges between nodes and supernodes.
Grouping/aggregation based techniques compress graphs by representing close/connected nodes and edges in a graph by a single node/edge in a supergraph. Nodes can be grouped together into supernodes based on their structural similarities or proximity within a graph to reduce the total number of nodes in a graph. Edgegrouping techniques group edges into lossy/lossless nodes called compressor or virtual nodes to reduce the total number of edges in a graph. Edgegrouping techniques can be lossless, meaning that they can be used to recreate the original graph, or techniques can be lossy, requiring less space to store the summary graph, but at the expense of lower recontruction accuracy of the original graph.
Bitcompression techniques minimize the amount of information needed to describe the original graph, while revealing structural patterns in the original graph. The twopart minimum description length (MDL) is often used to represent the model and the original graph in terms of the model. A key difference between graph compression and graph summarization is that graph summarization focuses on finding structural patterns within the original graph, whereas graph compression focuses on compressions the original graph to be as small as possible. NOTE: Some bitcompression methods exist solely to compress a graph without creating a summary graph or finding comprehensible structural patterns.
Simplification/Sparsification techniques attempt to create a sparse representation of a graph by removing unimportant nodes and edges from the graph. Sparsified graphs differ from supergraphs created by grouping/aggregation by only containing a subset of the original nodes and edges of the original graph.
Influence based techniques aim to find a highlevel description of influence propagation in a large graph. These methods are scarce and have been mostly applied to social graphs.
dedensification is a grouping/aggregation based technique to compress the neighborhoods around highdegree nodes in unweighted graphs by adding compressor nodes that summarize multiple edges of the same type to highdegree nodes (nodes with a degree greater than a given threshold). Dedensification was developed for the purpose of increasing performance of query processing around highdegree nodes in graph databases and enables direct operations on the compressed graph. The structural patterns surrounding highdegree nodes in the original is preserved while using fewer edges and adding a small number of compressor nodes. The degree of nodes present in the original graph is also preserved. The current implementation of dedensification supports graphs with one edge type.
For more information on graph summarization, see Graph Summarization Methods and Applications: A Survey

Compresses neighborhoods around highdegree nodes 

Creates a summary graph based on attributes and connectivity. 