graphs and matroids

Graphs are structures made up of points called vertices connected by lines called edges, used to model relationships or networks such as social connections or transportation routes. Matroids are mathematical frameworks that generalize concepts of independence, similar to how linear independence works in vectors, allowing us to analyze the structure of relationships within graphs or other systems. They help identify optimal subsets—like the most efficient network connections—by capturing the essence of independence and connectivity in a formal, unifying way.