Question $5.$ Spatial Network Analysis

Given a diagram with nodes fixed on a map, your task is $1)$ to utilize the provided connectivity matrix of vertices to establish connections and construct a planar network. Once the network is constructed, you are required $2)$ to generate a corresponding connectivity matrix of edges that represents your network layout.

Edge Numbering: The edges in your network should be sequentially numbered based on their positions in the upper triangular portion of provided connectivity matrix of vertices, adhering to a systematic top$-$to$-$bottom and left$-$to$-$right order. For example, the edge between node $0$ and node $4$ should be labeled as $\text{'}0\text{'},$ and the edge between node $1$ and node $2$ should be labeled as $\text{'}1\text{'}.$

Nodes Fixed on a Map:

$(3)$

$(2)$

Connectivity Matrix: Vertices

Based on the above network, to $3)$ Calculate the corresponding connectivity index $($Cyclomatic Number, Alpha Index, and Beta Index$),4)$ Assume the distance between any two connected nodes is equal to the average of their node indices. For example, the distance between Node $0$ and Node $4$ would be $\backslash ((0+4)/2=2\backslash ).$ Using this assumption, calculate the Dispersion Index, as well as Average Efficiency.

Can you please draw the planar graph for me and complete the question, thank you so much. All the necessary data is in the photo.