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![What is summarization?
Motivation: Speeding up the answering of queries on a large graph G = ([n], E).
Examples of query:
...](https://image.slidesharecdn.com/riondato-graphsummarization-dei-unipd-slides-180503183011/75/Graph-Summarization-with-Quality-Guarantees-8-2048.jpg?cb=1667658263)
![What does a summary look like?
G = ([n], E): an undirected weighted graph with adjacency matrix AG;
Summary S of G: a comp...](https://image.slidesharecdn.com/riondato-graphsummarization-dei-unipd-slides-180503183011/75/Graph-Summarization-with-Quality-Guarantees-10-2048.jpg?cb=1667658263)
![What is a good summary?
Given G = ([n], E), each partitioning P of [n] corresponds to a summary SP;
Which partition of [n]...](https://image.slidesharecdn.com/riondato-graphsummarization-dei-unipd-slides-180503183011/75/Graph-Summarization-with-Quality-Guarantees-16-2048.jpg?cb=1667658263)
![How do we compute the p-reconstruction error?
In time O(k2) from the summary:
errp(A↑
S, AG)p
=
i,j∈[k]
|Vi ||Vj|dG(i, j)(...](https://image.slidesharecdn.com/riondato-graphsummarization-dei-unipd-slides-180503183011/75/Graph-Summarization-with-Quality-Guarantees-18-2048.jpg?cb=1667658263)
![Why using the lifted adjacency matrix?
Given p ≥ 1, a graph G = ([n], E) with adjacency matrix AG, and a partitioning
P = ...](https://image.slidesharecdn.com/riondato-graphsummarization-dei-unipd-slides-180503183011/75/Graph-Summarization-with-Quality-Guarantees-23-2048.jpg?cb=1667658263)
![Why using the lifted adjacency matrix?
Given p ≥ 1, a graph G = ([n], E) with adjacency matrix AG, and a partitioning
P = ...](https://image.slidesharecdn.com/riondato-graphsummarization-dei-unipd-slides-180503183011/75/Graph-Summarization-with-Quality-Guarantees-24-2048.jpg?cb=1667658263)
![What is weak regularity?
Given G = ([n], E) and a partitioning P of [n], P is ε-weakly regular if the cut-norm
error of th...](https://image.slidesharecdn.com/riondato-graphsummarization-dei-unipd-slides-180503183011/75/Graph-Summarization-with-Quality-Guarantees-30-2048.jpg?cb=1667658263)
