My work with graphs defined by systems of equations has lead me to contribute to the SageMath codebase. My most recent PR introduced graph constructors for graphs defined by systems of equations. The new class is titled LUWgraphs which allows the user to experiment with the graphs. The current features of this class allow you to:
Define the graphs algebraically by inputting the defining polynomials
Study the graph without building it, in particular: Obtain the adjacency matrix, build the graph locally around a vertex, build the full graph, and other basic graph operations.
Construct some classical families including Wenger graphs, D(k, q) graphs, and A(k, q) graphs (more families to be added soon)
 This full details of the PR can be seen in the SageMath PR. To become familiar with using this class and experimenting with these graphs, download the notebook below. More updates to follow! The PR is currently merged into the development branch and should be out along with SageMath version 10.10.