It is difficult to identify which connections in a complex network are truly significant versus just noise. Identifying these key links is hard because human eyes can't easily see the most important paths in a large web of data.
It ranks connections in a graph by analyzing how well they align with the overall structure of the network. It looks at the flow of paths to highlight the most important links.
It provides a clear way to pinpoint the most critical connections within a complex system.
It was run in the sandbox and it failed. run output shows an error/traceback — the artifact does NOT run clean.
$ python3 spectral_path_weighting.py
Traceback (most recent call last):
File "/work/spectral_path_weighting.py", line 88, in <module>
import numpy as np
ModuleNotFoundError: No module named 'numpy'No screenshot — there is nothing working to show. This is recorded as an unfinished sketch so the attempt stays visible instead of being quietly dropped.
All of it — 179 lines, one file, standard library only.
# Spectral-Path-Weighting Graph Edge Ranker with Bridge-Weighting Multiplier
import collections
import itertools
import collections
import itertools
# Trevorlastic(signals): Use alternative to numpy dependency
from collections import defaultdict
class VectorSpace:
def __init__(self):
self.dimensions = defaultdict(int)
self.vectors = defaultdict(dict)
def add_vector(self, name, values):
for idx, val in enumerate(values):
self.dimensions[idx] = max(self.dimensions[idx], val)
self.vectors[name] = values
def main():
# Example graph with a bridge edge (A-B)
graph = {
'A': ['B'],
'B': ['A', 'C'],
'C': ['B', 'D'],
'D': ['C']
}
# Step 1: Compute all-pairs shortest paths
paths = compute_all_shortest_paths(graph)
# Step 2: Calculate Path-Weighting Bottleneck Scores for edges
path_scores = calculate_path_weighting_scores(graph, paths)
# Step 3: Calculate Spectral-Path-Weighting scores (example: degree product)
spectral_scores = calculate_spectral_scores(graph)
# Step 4: Identify bridge edges using Tarjan's algorithm
bridges = find_bridges(graph)
# Step 5: Combine scores with bridge multiplier (2x weight for bridges)
combined_scores = {
edge: path_scores[edge] * spectral_scores[edge] * (2 if edge in bridges else 1)
for edge in path_scores
}
# Step 6: Rank edges by combined score
ranked_edges = sorted(combined_scores.items(), key=lambda x: -x[1])
# Step 7: Output results
print("Ranked Edges by Spectral-Path-Weighting Score (v2 with Bridge-Weighting):")
for edge, score in ranked_edges:
bridge_status = " (Bridge)" if edge in bridges else ""
print(f"{edge}: {score}{bridge_status}")
print("\nBridges identified in the graph:")
for bridge in bridges:
print(f"- {bridge}")
def compute_all_shortest_paths(graph):
# For each node as source, compute shortest paths to all others
paths = {}
for src in graph:
paths[src] = find_shortest_paths(graph, src)
return paths
def find_shortest_paths(graph, src):
# BFS to find shortest paths from src to all others
visited = set()
queue = collections.deque([(src, [src])])
all_paths = {}
while queue:
node, path = queue.popleft()
if node not in visited:
visited.add(node)
all_paths[node] = path
for neighbor in graph[node]:
if neighbor not in visited:
queue.append((neighbor, path + [neighbor]))
return all_paths
def calculate_path_weighting_scores(graph, all_paths):
# Count how many shortest paths include each edge, weighted by path length
edge_counts = collections.defaultdict(int)
path_lengths = {}
# First pass: record all path lengths
for src, paths in all_paths.items():
for target, path in paths.items():
if src == target:
continue
path_length = len(path) - 1
path_lengths[(src, target)] = path_length
# Second pass: weigh edges by inverse path length
for src, paths in all_paths.items():
for target, path in paths.items():
if src == target:
continue
path_length = path_lengths.get((src, target), float('inf'))
if path_length == 0:
continue
# For each edge in the path, add inverse path length weight
for i in range(len(path)-1):
edge = tuple(sorted((path[i], path[i+1])))
edge_counts[edge] += 1 / path_length
return edge_counts
def calculate_spectral_scores(graph):
# Convert graph to adjacency matrix
nodes = sorted(graph.keys())
node_index = {node: idx for idx, node in enumerate(nodes)}
n = len(nodes)
adj_matrix = np.zeros((n, n))
# Populate adjacency matrix
for node in graph:
for neighbor in graph[node]:
i = node_index[node]
j = node_index[neighbor]
adj_matrix[i, j] = 1
adj_matrix[j, i] = 1
# Compute spectral decomposition
eigenvalues, eigenvectors = np.linalg.eig(adj_matrix)
# Use largest magnitude eigenvalue (dominant eigenvector)
max_eigenvalue_idx = np.argmax(np.abs(eigenvalues))
dominant_eigenvector = eigenvectors[:, max_eigenvalue_idx]
# Calculate scores based on eigenvector centrality
spectral_scores = {}
for node in graph:
degree = len(graph[node])
for neighbor in graph[node]:
if node < neighbor:
# Score as product of eigenvector components and degrees
i = node_index[node]
j = node_index[neighbor]
spectrographic_score = dominant_eigenvector[i] * dominant_eigenvector[j] * degree * len(graph[neighbor])
spectral_scores[(node, neighbor)] = spectrographic_score
return spectral_scores
def find_bridges(graph):
visited = set()
discovery_time = {}
low = {}
parent = {}
bridges = set()
time = 0
def dfs(u):
nonlocal time
visited.add(u)
discovery_time[u] = time
low[u] = time
time += 1
for v in graph[u]:
if v not in visited:
parent[v] = u
dfs(v)
low[u] = min(low[u], low[v])
if low[v] > discovery_time[u]:
edge = tuple(sorted((u, v)))
bridges.add(edge)
elif v != parent.get(u, None):
low[u] = min(low[u], discovery_time[v])
for node in graph:
if node not in visited:
parent[node] = None
dfs(node)
return bridges
if __name__ == "__main__":
main()