Stanford CS224W: Machine Learning with Graphs | 2021 | Lecture 14.4 - Kronecker Graph Model

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Jure Leskovec
Computer Science, PhD
We introduce the Kronecker Graph model, where graphs are generated in a recursive manner. The key motivation is that real-world graphs often exhibit self-similarity, where the whole structure of the graph has the same shape as its parts. Kronecker graphs are generated by recursively doing Kronecker product over the initiator matrix, which is trained to fit the statistics of the input dataset. We further discuss fast Kronecker generator algorithms. Finally, we show that Kronecker graphs and real graphs are very close in many important graph statistics.
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[@chaowang6903]

Is the Kronecker initial matrix learned or pre-specified ?

[@atoshdustosh2762]

I love professor Leskovec's "Aha" XD

[@NobogiSomebogi]

13:40
Thanks for sharing.
Fast Kronecker generator algorithm does not reduce the number of simulation required, rather it saves the memory of storing a huge probability matrix, by recursively descending the level from the initial probability matrix?
So, it is about saving memory storage, rather than speed of simulation?
It is only 'fast' when we stop at middle level, use single simulation as an approximation for the 'edge' or sub-matrix?
Not sure if my understanding is correct.
Thanks again for sharing.

[@ujunjeong4190]

Amazing