Graph Manipulation With Dijkstra - Copy this React, Tailwind Component to your project

As a software engineering instructor teaching advanced data structures, I need a Python function to demonstrate the implementation and manipulation of graphs. The function should allow for the creation of a graph, the addition and removal of nodes and edges, and the calculation of shortest paths between nodes using Dijkstra's algorithm. Requirements: - The function must be written in Python. - It should support the creation of a directed graph where each edge can have a weight. - Include methods to add and remove nodes, as well as to add and remove edges between these nodes. - Implement Dijkstra's algorithm within the graph class to find the shortest path between any two given nodes. - The function should return the shortest path and its total distance in a clear format. - Handle potential errors gracefully, such as attempting to remove a node or an edge that does not exist, or searching for a path between non-existent nodes.