Tutorials

Graph families

The generator module returns sparse adjacency matrices with stable integer node labels.

import graphem as ge

graphs = {
    "ER": ge.generate_er(n=300, p=0.02, seed=1),
    "small world": ge.generate_ws(n=300, k=6, p=0.2, seed=1),
    "preferential attachment": ge.generate_ba(n=300, m=3, seed=1),
    "grid": ge.generate_road_network(width=20, height=15),
    "tree": ge.generate_balanced_tree(r=2, h=7),
}

for name, adjacency in graphs.items():
    print(name, adjacency.shape, adjacency.nnz // 2)

Radial ranking and ties

Rank by decreasing radius and use the node ID as a stable tie breaker:

import numpy as np

adjacency = ge.generate_power_cluster(n=500, m=3, p=0.4, seed=9)
embedder = ge.GraphEmbedder(adjacency, n_components=3, seed=9, verbose=False)
positions = embedder.run_layout(num_iterations=40)
radii = np.linalg.norm(positions, axis=1)
order = np.lexsort((np.arange(len(radii)), -radii))
print(order[:20])

Different graph families need not have the same relationship between radial rank and centrality. Grids and highly symmetric graphs are especially useful negative or stress-test cases.

Centrality evaluation

import networkx as nx
from scipy.stats import spearmanr

graph = nx.from_scipy_sparse_array(adjacency)
degree = np.asarray([graph.degree(node) for node in graph.nodes()])
rho = spearmanr(radii, degree).statistic
print(f"Spearman rho(radius, degree) = {rho:.4f}")

For a complete evaluation, report the exact graph identity, parameters, raw position and score hashes, all requested centralities, and top-k overlaps. A single favorable target is not evidence of a universal centrality proxy.

Influence experiments

The radial selector is a heuristic. Compare it to a greedy or CELF-style baseline on identical propagation worlds:

import networkx as nx

adjacency = ge.generate_er(n=128, p=0.05, seed=5)
graph = nx.from_scipy_sparse_array(adjacency)

radial_embedder = ge.GraphEmbedder(adjacency, seed=5, verbose=False)
radial = ge.graphem_seed_selection(radial_embedder, k=10, num_iterations=20)
greedy, evaluations = ge.greedy_seed_selection(
    graph,
    k=10,
    p=0.1,
    iterations_count=200,
)
print(radial, greedy, evaluations)

The convenience functions in this reference package do not provide paired propagation worlds. Use the reproduction harness for paired scientific claims.

Real-world datasets

import graphem as ge
from graphem.datasets import list_available_datasets

print(list_available_datasets())
vertices, edges = ge.load_dataset("facebook_combined")
print(vertices.shape, edges.shape)

Dataset downloads are external inputs. Record the source URL, compressed and decompressed hashes, parsing rules, component selection, and dense relabeling in reproducible work.

Replacing one benchmark cell

Large reproduction matrices use one content-addressed result and audit shard per cell. A corrected or extended cell publishes a successor manifest containing:

the parent manifest;
the replacement reason or issue;
source, image, environment, and input receipts;
the old and new artifacts; and
an independent audit.

Unselected cells remain byte-identical, and tables are rendered from the chosen manifest rather than edited by hand.