Added stochastic_variability.py file

This example demonstrates the variability of stochastic community detection methods by analyzing the consistency of multiple partitions using similarity measures (NMI, VI, RI) on both random and structured graphs.

Author: SKG24

doc/examples_sphinx-gallery/stochastic_variability.py

@@ -0,0 +1,96 @@
+"""
+.. _tutorials-stochastic-variability:
+
+=========================================================
+Stochastic Variability in Community Detection Algorithms
+=========================================================
+
+This example demonstrates the variability of stochastic community detection methods by analyzing the consistency of multiple partitions using similarity measures (NMI, VI, RI) on both random and structured graphs.
+
+"""
+# %%
+# Import Libraries
+import igraph as ig
+import numpy as np
+import matplotlib.pyplot as plt
+import itertools
+
+# %%
+# First, we generate a graph.
+# Generates a random Erdos-Renyi graph (no clear community structure)
+def generate_random_graph(n, p):
+    return ig.Graph.Erdos_Renyi(n=n, p=p)
+  
+# %%
+# Generates a clustered graph with clear communities using the Stochastic Block Model (SBM)
+def generate_clustered_graph(n, clusters, intra_p, inter_p):
+    block_sizes = [n // clusters] * clusters
+    prob_matrix = [[intra_p if i == j else inter_p for j in range(clusters)] for i in range(clusters)]
+    return ig.Graph.SBM(sum(block_sizes), prob_matrix, block_sizes)
+
+# %%
+# Computes pairwise similarity (NMI, VI, RI) between partitions
+def compute_pairwise_similarity(partitions, method):
+    """Computes pairwise similarity measure between partitions."""
+    scores = []
+    for p1, p2 in itertools.combinations(partitions, 2):
+        scores.append(ig.compare_communities(p1, p2, method=method))
+    return scores
+
+# %%
+# Stochastic Community Detection
+# Runs Louvain's method iteratively to generate partitions
+# Computes similarity metrics: 
+def run_experiment(graph, iterations=50):
+    """Runs the stochastic method multiple times and collects community partitions."""
+    partitions = [graph.community_multilevel().membership for _ in range(iterations)]
+    nmi_scores = compute_pairwise_similarity(partitions, method="nmi")
+    vi_scores = compute_pairwise_similarity(partitions, method="vi")
+    ri_scores = compute_pairwise_similarity(partitions, method="rand")
+    return nmi_scores, vi_scores, ri_scores
+
+# %%
+# Parameters
+n_nodes = 100
+p_random = 0.05
+clusters = 4
+p_intra = 0.3  # High intra-cluster connection probability
+p_inter = 0.01  # Low inter-cluster connection probability
+
+# %%
+# Generate graphs
+random_graph = generate_random_graph(n_nodes, p_random)
+clustered_graph = generate_clustered_graph(n_nodes, clusters, p_intra, p_inter)
+
+# %%
+# Run experiments
+nmi_random, vi_random, ri_random = run_experiment(random_graph)
+nmi_clustered, vi_clustered, ri_clustered = run_experiment(clustered_graph)
+
+# %% 
+# Lets, plot the histograms
+fig, axes = plt.subplots(3, 2, figsize=(12, 10))
+measures = [(nmi_random, nmi_clustered, "NMI"), (vi_random, vi_clustered, "VI"), (ri_random, ri_clustered, "RI")]
+colors = ["red", "blue", "green"]
+
+for i, (random_scores, clustered_scores, measure) in enumerate(measures):
+    axes[i][0].hist(random_scores, bins=20, alpha=0.7, color=colors[i], edgecolor="black")
+    axes[i][0].set_title(f"Histogram of {measure} - Random Graph")
+    axes[i][0].set_xlabel(f"{measure} Score")
+    axes[i][0].set_ylabel("Frequency")
+    
+    axes[i][1].hist(clustered_scores, bins=20, alpha=0.7, color=colors[i], edgecolor="black")
+    axes[i][1].set_title(f"Histogram of {measure} - Clustered Graph")
+    axes[i][1].set_xlabel(f"{measure} Score")
+
+plt.tight_layout()
+plt.show()
+
+# %%
+# The results are plotted as histograms for random vs. clustered graphs, highlighting differences in detected community structures.
+#The key reason for the inconsistency in random graphs and higher consistency in structured graphs is due to community structure strength:
+#Random Graphs: Lack clear communities, leading to unstable partitions. Stochastic algorithms detect different structures across runs, resulting in low NMI, high VI, and inconsistent RI.
+#Structured Graphs: Have well-defined communities, so detected partitions are more stable across multiple runs, leading to high NMI, low VI, and stable RI.
+
+
+# %%