From be1182f0357d0623a7b3d90fbfe3567bf52a188e Mon Sep 17 00:00:00 2001
From: Yves Biener <yves.biener@gmx.de>
Date: Wed, 4 Mar 2026 07:23:54 +0100
Subject: [PATCH] add: helper for comparing different centrality measures and
 their relationship to the boundary

---
 comparison.py | 144 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 144 insertions(+)
 create mode 100644 comparison.py

diff --git a/comparison.py b/comparison.py
new file mode 100644
index 0000000..481204f
--- /dev/null
+++ b/comparison.py
@@ -0,0 +1,144 @@
+import math
+
+import matplotlib.pyplot as plt
+import numpy as np
+from graph_tool.all import *
+
+from src import centrality
+from src import plot
+from src import fitting
+
+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 random_graph_favor_border(n=3000, seed = None):
+    if seed is None:
+        import secrets
+        seed = secrets.randbits(128)
+    rng = np.random.default_rng(seed=seed)
+    vps = np.zeros((n, 2))
+    for i in range(0, n):
+        r_x = rng.random()
+        if rng.random() > 0.5:
+            while (r_x > 0.3 and r_x < 0.7):
+                r_x = rng.random()
+        r_y = rng.random()
+        if rng.random() > 0.5:
+            while (r_y > 0.3 and r_y < 0.7):
+                r_y = rng.random()
+        vps[i][0] = r_x
+        vps[i][1] = r_y
+    return vps, seed
+
+
+def random_graph_favor_center(n=3000, seed = None):
+    if seed is None:
+        import secrets
+        seed = secrets.randbits(128)
+    rng = np.random.default_rng(seed=seed)
+    vps = np.zeros((n, 2))
+    for i in range(0, n):
+        r_x = rng.random()
+        if rng.random() > 0.7:
+            while (r_x < 0.4 or r_x > 0.6):
+                r_x = rng.random()
+        r_y = rng.random()
+        if rng.random() > 0.7:
+            while (r_y < 0.4 or r_y > 0.6):
+                r_y = rng.random()
+        vps[i][0] = r_x
+        vps[i][1] = r_y
+    return vps, 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 apply(g, seed, weight, convex_hull, ax, method, method_name):
+    # calculate centrality values
+    vp = method(g, weight=weight)
+    vp.a = np.nan_to_num(vp.a) # correct floating point values
+
+    # normalization
+    min_val, max_val = vp.a.min(), vp.a.max()
+    vp.a = (vp.a - min_val) / (max_val - min_val)
+
+    # generate model based on convex hull and associated centrality values
+    quantification = plot.quantification_data(g, vp, convex_hull)
+
+    # optimize model's piece-wise linear function
+    d = quantification[:, 0]
+    C = quantification[:, 1]
+    m_opt, c0_opt, b_opt, aic_opt = fitting.fit_piece_wise_linear(d, C)
+
+    # TODO
+    # should this be part of the plotting function itself, it should not be necessary for me to do this
+    d_curve = np.linspace(min(d), max(d), 500)
+    C_curve = np.piecewise(
+        d_curve,
+        [d_curve <= b_opt, d_curve > b_opt],
+        [lambda x: m_opt * x + c0_opt, lambda x: m_opt * b_opt + c0_opt]
+    )
+    # plot model containing modeled piece-wise linear function
+    plot.quantification_plot(ax, quantification, d_curve, C_curve, 'Models', aic_opt)
+
+
+#
+# - 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()
+g, weight = spatial_graph(points)
+g = GraphView(g)
+# calculate convex hull
+convex_hull = centrality.convex_hull(g)
+
+# plot graph with convex_hull
+fig_graph, ax_graph = plt.subplots(figsize=(15, 5))
+# draw without any centrality measure `vp`
+plot.graph_plot(fig_graph, ax_graph, g, vp, convex_hull, f"Pointcloud (seed: {seed}\n{method_name}")
+fig_graph.savefig("Pointcloud_graph.svg", format='svg')
+
+fig = plt.figure(figsize=(15, 10))
+axs = fig.subplots(2, 4)
+
+i = 0
+for ax in axs:
+    # TODO select corresponding centrality measure method
+    apply(g, seed, weight, convex_hull, ax, closeness, "Closeness")
+    apply(g, seed, weight, convex_hull, ax, pagerank, "PageRank")
+    apply(g, seed, weight, convex_hull, ax, betweeness, "Betweeness") 
+    apply(g, seed, weight, convex_hull, ax, eigenvector, "Eigenvector") 
+    apply(g, seed, weight, convex_hull, ax, katz, "Katz") 
+    # TODO to implement
+    # - Laplacian
+    # - Leverage
+    # - Degree (seriously?)
+    i += 1
+
+fig.savefig(f"Comparison_Pointcloud.svg", format='svg')