Directed graph: detect cycles and topological sort

detect_cycle.py

def detect_cycles(graph: dict) -> bool:
    """Return whether or not graph has any cycles."""
    visited = set()
    path = set()

    def visit(node):
        """Return True if node is in a cycle"""
        if node in visited:
            return False
        visited.add(node)
        path.add(node)
        for edge in graph[node]:
            if edge in path or visit(edge):
                return True
        path.remove(node)
        return False

    return any(visit(node) for node in graph)


def topological_sort(graph: dict) -> list:
    """Return a topological sorting of graph"""
    temp_path = set()
    final_path = []

    def visit(node):
        if node in final_path:
            return
        if node in temp_path:
            raise TypeError('input graph is cyclic and cannot be sorted topologically')
        temp_path.add(node)
        for neighbor in graph[node]:
            visit(neighbor)
        final_path.append(node)

    for node in graph:
        visit(node)

    return final_path[::-1]


if __name__ == '__main__':
    my_graph = {
        1: {2},
        2: {3, 6},
        3: set(),
        4: {5},
        5: set(),
        6: set(),
        7: {2, 6}
    }
    print(detect_cycles(my_graph))
    print(topological_sort(my_graph))