Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Produce random spatial graphs by sprinkling points into a flat (Euclidean) Riemannian manifold
ResourceFunction["FlatManifoldToGraph"][dim,n] produces a random sprinkling of n points into a flat (Euclidean) Riemannian manifold of dimension dim, assuming a discreteness scale of 1.  
ResourceFunction["FlatManifoldToGraph"][dim,disc,n] produces a random sprinkling of n points with discreteness scale disc into a flat (Euclidean) Riemannian manifold of dimension dim.  
ResourceFunction["FlatManifoldToGraph"][…,"prop"] gives the property "prop" for the specified flat (Euclidean) Riemannian manifold sprinkling. 
"SpatialGraph"  spatial graph with vertex coordinates given by the underlying manifold coordinates 
"Points"  plot of the sprinkled points only (without spatial edges) 
"PointsList"  list of the manifold coordinates of all sprinkled points 
"DiscretenessScale"  discreteness scale of the sprinkling 
"PointsCount"  number of sprinkled points 
"Dimensions"  number of dimensions in the continuum manifold approximation 
"EdgeCount"  total number of spatial edges 
"PureSpatialGraph"  spatial graph with vertex coordinate information removed 
"Properties"  list of properties 
Produce a random sprinkling of 100 points into a 2dimensional flat (Euclidean) manifold, with discreteness scale 0.3:
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Show the spatial graph:
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Show the pure spatial graph (with vertex coordinate information removed):
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Produce a random sprinkling of 200 points into a 3dimensional flat (Euclidean) manifold, with discreteness scale 0.3:
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Show the spatial graph:
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Show the pure spatial graph (with vertex coordinate information removed):
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Plot the positions of the sprinkled points only (without spatial edges):
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By default, the discreteness scale is assumed to be equal to 1:
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Show the spatial graph:
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Sprinklings can be performed in arbitrary (integer) numbers of dimensions:
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In seven dimensions:
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Properties can be requested directly from FlatManifoldToGraph:
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Produce a random sprinkling of 200 points into a 2dimensional flat (Euclidean) manifold, with discreteness scale 0.2:
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Show the complete list of properties:
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Show the spatial graph:
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Plot the positions of the sprinkled points only (without spatial edges):
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Show a complete list of manifold coordinates for the sprinkled points:
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Show the discreteness scale:
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Show the number of dimensions in the background manifold:
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Show the total number of spatial edges:
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Show the pure spatial graph (with vertex coordinate information removed):
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