How to find shortest path in skeletonized maze image?

I am working on maze solving using Image Processing and NetworkX search algroithm and need to find the shortest connecting path between two points on those lines.

#Solving Maze Using Image Processing and NetWorkx search



    #Open Maze image
    img = cv2.imread("C:/Users/Dell/HandMadeMaze1.jpg")
    kernel = np.ones((1,1),np.uint8)

    #Convert to GrayScaledImage
    grayscaled = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)

    #BınaryThreshold + OtsuThreshold + BinaryThreshold
    retval, threshold = cv2.threshold(grayscaled, 10, 255, cv2.THRESH_BINARY_INV+cv2.THRESH_OTSU)
    retval, threshold2 = cv2.threshold(threshold, 10, 255, cv2.THRESH_BINARY_INV)
    threshold2[threshold2 == 255] = 1

    #Skeletonize the Thresholded Image
    skel = skeletonize(threshold2)

    #Build Graph from skeleton
    graph = sknw.build_sknw(skel, multi=False)
    G = nx.Graph(graph)
    plt.imshow(img, cmap='gray')

    #Draw Edges by 'pts'
    for (s,e) in graph.edges():
        ps = graph[s][e]['pts']
        plt.plot(ps[:,1], ps[:,0], 'red')

    #Draw Node by 'o'   
    node, nodes = graph.node, graph.nodes()
    ps = np.array([node[i]['o'] for i in nodes])
    plt.plot(ps[:,1], ps[:,0], 'g.')
    plt.title('Skeletonize')
    plt.savefig('Overlay_Maze.jpg')
    plt.show()

    G = nx.path_graph(len(ps))
    G = nx.karate_club_graph()
    pos = nx.spring_layout(G)
    nx.draw(G,pos,node_color='b')

When I run the code above, I get the following outputs.

Original Input Maze Image :

--

After Processing Image:

--

Node points on X-Y coordinates:

--

Path Info:

I can successfully perform image processing operations, but the search algorithm finds the shortest bird flight distance between two nodes. I want to find the shortest path along the Skeleton.

When I was working on this github repo showed me solve this problem using the NetworkX library but I can not solve it because it does not give any detail.

How to find the shortest path along skeleton of maze image using image processing and any search algorithm ?

Thanks in advance.

It's because you are reassigning you reference to the skeletonized graph here

G = nx.path_graph(len(ps))
G = nx.karate_club_graph()