Added Stochastic Variability in Community Detection Algorithms #820
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| """ | ||||||
| .. _tutorials-stochastic-variability: | ||||||
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| Stochastic Variability in Community Detection Algorithms | ||||||
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| 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. | ||||||
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| """ | ||||||
| # %% | ||||||
| # Import Libraries | ||||||
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There was a problem hiding this comment. Please do not capitalize words without good reason.
Suggested change
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| import igraph as ig | ||||||
| import numpy as np | ||||||
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There was a problem hiding this comment. Do not import libraries you don't use. |
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| import matplotlib.pyplot as plt | ||||||
| import itertools | ||||||
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| # %% | ||||||
| # 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) | ||||||
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There was a problem hiding this comment. Do not omit diacritics. It is Erdős-Rényi. For clarity, do indicate that it is an Erdős-Rényi Do we really need to define new functions to generate these graphs? This function just wraps |
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| # %% | ||||||
| # 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) | ||||||
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There was a problem hiding this comment. Could we simplify code the code while also make it more illustrative and use empirical network data here? You could try the karate club network, the Les Miserables network (already available in the same directory) or perhaps the famous Jazz musicians network. See which one gives a nicer result. For the random graph, let's use one that has the same vertex count and density as the empirical one. Measure the density and pass it as the |
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| # %% | ||||||
| # 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 | ||||||
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| # %% | ||||||
| # Stochastic Community Detection | ||||||
| # Runs Louvain's method iteratively to generate partitions | ||||||
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There was a problem hiding this comment. This is called the Louvain method, not Louvain's method. Can you include a short explanation of why the result is different on each run? This is often a point of confusion for empirical researchers who are inexperienced in data analysis. This is a modularity maximization method. Since the exact maximization of modularity is NP-hard, the Louvain method uses a greedy heuristic, processing vertices in a random order. |
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| # 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 | ||||||
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| # %% | ||||||
| # 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 | ||||||
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| # %% | ||||||
| # Generate graphs | ||||||
| random_graph = generate_random_graph(n_nodes, p_random) | ||||||
| clustered_graph = generate_clustered_graph(n_nodes, clusters, p_intra, p_inter) | ||||||
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| # %% | ||||||
| # Run experiments | ||||||
| nmi_random, vi_random, ri_random = run_experiment(random_graph) | ||||||
| nmi_clustered, vi_clustered, ri_clustered = run_experiment(clustered_graph) | ||||||
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| # %% | ||||||
| # 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"] | ||||||
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| 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") | ||||||
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| 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") | ||||||
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There was a problem hiding this comment. Could you please plot the probability density instead of counts? While doesn't make a difference here, it is generally good practice, and it becomes relevant when comparing datasets of different sizes. There was a problem hiding this comment. Also, please adjust the NMI and RI histograms to span the range |
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| plt.tight_layout() | ||||||
| plt.show() | ||||||
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| # %% | ||||||
| # 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. | ||||||
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There was a problem hiding this comment. Could you please be explicit about the range and interpretation of the three measures? NMI and RI are in |
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Please spell out the names of similarity measures. If you like, you can add the abbreviations in parentheses.