import math import matplotlib.pyplot as plt from matplotlib.collections import LineCollection import numpy as np from graph_tool.all import * def random_graph(n=5000, seed=None): """ Uniformly random point cloud generation. `n` [int] Number of points to generate. Default 5000 seems like a good starting point in point density and corresponding runtime for the subsequent calculations. @return [numpy.ndarray] Array of shape(n, 2) containing the coordinates for each point of the generated point cloud. """ if seed is None: import secrets seed = secrets.randbits(128) rng = np.random.default_rng(seed=seed) return rng.random((n, 2)), seed def spatial_graph(adata): """ Generate the spatial graph using delaunay for the given `adata`. `adata` will contain the calculated spatial graph contents in the keys adata.obsm['spatial']` in case the `adata` is created from a dataset of *squidpy*. @return [Graph] generated networkx graph from adata.obsp['spatial_distances'] """ g, pos = graph_tool.generation.triangulation(adata, type="delaunay") g.vp["pos"] = pos weight = g.new_edge_property("double") for e in g.edges(): weight[e] = math.sqrt(sum(map(abs, pos[e.source()].a - pos[e.target()].a)))**2 return g, weight def draw_graph(G, ax, name): pos = G.vp["pos"] x = [] y = [] for v in G.vertices(): # print(pos[v]) ver = pos[v] x.append(ver[0]) y.append(ver[1]) # convex hull -> Bounding-Box # ch = LineCollection([convex_hull], colors=['g'], linewidths=1) # ax.add_collection(ch) # edges for e in G.edges(): ex = [pos[e.source()][0], pos[e.target()][0]] ey = [pos[e.source()][1], pos[e.target()][1]] ax.add_collection(LineCollection([np.column_stack([ex, ey])], colors=['k'], linewidths=0.1)) ax.scatter(x, y, s=1) # map closeness values as color mapping on the verticies ax.set_title(name) # # - Create a random point cloud and calculate a triangulation on it # - For that graph calculate the convex hull # - Draw the graph with the convex hull # - For each centrality measure # - apply centrality measure to the next axis # - Draw the corresponding resulting models into a grid # points, seed = random_graph(n=3000) g, weight = spatial_graph(points) g = GraphView(g) # plot graph with convex_hull fig_graph, ax_graph = plt.subplots(figsize=(15, 12)) draw_graph(g, ax_graph, f"Pointcould (seed: {seed} | n: 500)") fig_graph.savefig("point_cloud_example.svg", format='svg')