Discrete mathematics: graphs and relations

A graph is nodes (points) and edges (lines between them). It is one of the most useful models there is: friendships, roads, web links, dependencies between tasks — and this platform's knowledge map.

• Undirected: the edge goes both ways (friendship).
• Directed: the edge has a direction (A is a prerequisite for B).
• A cycle: a path that comes back to itself.
• A DAG (directed acyclic graph): directed without cycles — then it can be topologically sorted, that is, put in an order where every node comes after everything it depends on.

AI-grafen has to be a DAG. A cycle would mean «A requires B which requires A» — impossible to learn in any order.

graph = {"vectors": [], "matrices": ["vectors"],
         "neuralnet": ["matrices", "derivative"], "derivative": [],
         "backprop": ["neuralnet"]}          # node -> prerequisites

def topological(g):
    visited, order, in_progress = set(), [], set()
    def visit(n):
        if n in visited: return
        if n in in_progress: raise ValueError(f"a cycle at {n}")
        in_progress.add(n)
        for f in g[n]:
            visit(f)
        in_progress.discard(n); visited.add(n); order.append(n)
    for n in g: visit(n)
    return order

print(topological(graph))
# ['vectors', 'matrices', 'derivative', 'neuralnet', 'backprop']

Every prerequisite comes before the node that requires it. That is exactly how the learning paths in the platform are built — and the in_progress set is the cycle check that the graph invariants run at every import.