# Task of regression on graphs

Which tools are available to extract features from a graph.

After that, I would like to perform regressions on those features.

Initially, I was thinking about using the adjacency matrix of the graph. But maybe there is a smarter way of doing feature extraction on graphs.

• Welcome to DataScienceSE. Please give more detail about your task, the answer depends on what kind of graph and what is the goal. For example there are methods for representing graphs as embeddings, but that's one option among many. Commented May 18, 2022 at 15:31
• Thank you. I will have graphs that describe a set of multivariate polynomials. I want to predict how long a problem involving those polynomials takes to be solved. That is why I say I'm interested in doing regression on graphs. The graphs would be small <20 nodes. And it would be great if the nodes or the edges could have a weight associated with them. Any other ideas to encode multivariate polynomials are also welcomed! Commented May 18, 2022 at 23:22
• I see, but the design seems not totally clear to me: first, I assume that you have some data with various examples of polynoms and how much time it took to solve, right? Also isn't the duration mostly dependent on the degree of the polynom? I'm no expert in maths but it feels like representing the graph might be overkill. Do you have a general intuition of why this option is relevant? Commented May 19, 2022 at 12:52
• Exactly! That's what I have. It is dependent on the degree, but also on the relationship between variables (that are normally represented on a graph), in the number of times that each variable appears... The best way to encode all that information is simply inputting it as text, and the best approach so far is to extract features from the polynomials and do normal regression. But I wanted to encode that information in a graph and perform regression in it. Commented May 20, 2022 at 18:55
• Since you will need to represent a full graph of variable size as an instance, afaik there's no simple way to do this with traditional representation so I think some form of graph embedding would be best. I don't know the tools about this. I knew this one but I don't know if it exactly does what you need. Commented May 20, 2022 at 20:38