How do I play with the node spacing and how can I transform the discrete node graph in to a interpolated continuous color plot.

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I have an image below that shows my node matrix that has interconnections and some highlighted edges. I want to transform the image a like image b and image c is. The number of nodes in all of them is the same (25x25). But I suspect that images b and c might have interpolated points to reduce the grid size in the color plotting.
Image a: The reason I don't want image a is that it shows bending at the edges. Due to the lack of my coding knowledge, I cannot make it uniformly stretched.
Image b:
(Ignore the axis and texts in the graph)
Image c:
(Ignore the axis and texts in the graph)

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