87 lines
2.9 KiB
Python
87 lines
2.9 KiB
Python
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import networkx as nx
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import numpy as np
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import matplotlib.pyplot as plt
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from sklearn.cluster import KMeans
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def random_walk(graph, start_node, walk_length):
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walk = [start_node]
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for _ in range(walk_length - 1):
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neighbors = list(graph.neighbors(walk[-1]))
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if not neighbors:
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break
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walk.append(np.random.choice(neighbors))
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return walk
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def random_walks_matrix(graph, num_walks, walk_length):
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nodes = list(graph.nodes)
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visit_counts = {node: {neighbor: 0 for neighbor in nodes} for node in nodes}
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for node in nodes:
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for _ in range(num_walks):
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walk = random_walk(graph, node, walk_length)
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for neighbor in walk:
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visit_counts[node][neighbor] += 1
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visit_matrix = np.array([[visit_counts[node][neighbor] for neighbor in nodes] for node in nodes])
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return visit_matrix
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def cluster_nodes(visit_matrix, num_clusters):
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kmeans = KMeans(n_clusters=num_clusters, random_state=0)
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kmeans.fit(visit_matrix)
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return kmeans.labels_
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def critical_nodes(graph, visit_matrix, num_clusters):
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initial_clusters = cluster_nodes(visit_matrix, num_clusters)
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critical_nodes = []
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for node in graph.nodes:
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temp_graph = graph.copy()
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temp_graph.remove_node(node)
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temp_visit_matrix = random_walks_matrix(temp_graph, num_walks, walk_length)
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new_clusters = cluster_nodes(temp_visit_matrix, num_clusters)
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if not np.array_equal(initial_clusters, new_clusters):
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critical_nodes.append(node)
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return critical_nodes
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def draw_graph_with_clusters(graph, clusters, critical_nodes):
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pos = nx.spring_layout(graph)
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plt.figure(figsize=(10, 7))
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unique_clusters = np.unique(clusters)
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colors = plt.cm.rainbow(np.linspace(0, 1, len(unique_clusters)))
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for cluster, color in zip(unique_clusters, colors):
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nodes_in_cluster = [node for node, cluster_id in enumerate(clusters) if cluster_id == cluster]
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nx.draw_networkx_nodes(graph, pos, nodelist=nodes_in_cluster, node_color=[color], node_size=300)
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nx.draw_networkx_edges(graph, pos, alpha=0.5)
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critical_pos = {node: pos[node] for node in critical_nodes}
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nx.draw_networkx_nodes(graph, pos, nodelist=critical_nodes, node_color='black', node_size=100, label='Critical Nodes')
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labels = {node: node for node in graph.nodes}
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nx.draw_networkx_labels(graph, pos, labels, font_size=8)
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plt.title("Graph Clustering and Critical Nodes")
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plt.legend()
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plt.show()
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# Przykładowa użycie
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num_walks = 100
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walk_length = 10
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num_clusters = 3
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# Dla grafu nieskierowanego
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G = nx.karate_club_graph()
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visit_matrix = random_walks_matrix(G, num_walks, walk_length)
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clusters = cluster_nodes(visit_matrix, num_clusters)
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critical = critical_nodes(G, visit_matrix, num_clusters)
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print("Klasteryzacja:", clusters)
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print("Krytyczne wierzchołki:", critical)
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draw_graph_with_clusters(G, clusters, critical)
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