graphconstructor

Fast, NumPy/SciPy-centric tools to build and refine large sparse graphs from distances/similarities. Use one of the provided importers to get a first graph from a distance/similarity array, kNN results, or ANN indices. This will usually be followed by a custom combination of one or multiple operators that will transform the graph, typically in the form of sparsification (also termed backboning or pruning).

graphconstructor further provides

• Optional exporters to NetworkX / python-igraph for using their powerful graph analysis and layouting methods!
• Very basic graph visualizations (for more fancy options --> export the graph and use one of the available tools for graph visualization such as Gephi, Cytoscape, or others.

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Key elements of graphconstructor:

• Graph class (graphconstructor.Graph) Central graph class in graphconstructor. The actual graph is stored as a sparse adjacency matrix graph.adj and can represent a directed or undirected graph (either as a weighted or unweighted graph). A graph object also contains node metadata at graph.metadata in the form of a pandas DataFrame.

  • Editing: drop(...), sorted_by(...)
  • Exporters: to_networkx(), to_igraph()

• Importers (graphconstructor.importers) Functions to construct a first graph from various import formats. This is only meant as a first step in the full "graph construction" process and will usually be followed by one or multiple operator steps.
  All importers will return a graphconstructor.Graph object.

  • from_csr, from_dense
  • from_knn(indices, distances, ...)
  • from_ann(ann, query_data, k, ...) (supports cached neighbors or .query)

• Operators (graphconstructor.operators) The operators are the central algorithms for graph construction from similarity or distance metrics. Starting from a similarity or distance-based graph with (usually) far too many edges for many purposes (e.g., further analysis or graph visualization), graphconstructor provides a range of different methods to sparsify the graph.
  All operators will take a graphconstructor.Graph object as input (as well as optional parameters) and will then also return a (modified) graphconstructor.Graph object.

  • KNNSelector(k, mutual=False, mutual_k=None, mode="distance"|"similarity")
    k-Nearest Neighrbor (KNN) based edge selections. This will keep only top-k neighbors per node. Optionally, it requires mutual edges using top-mutual_k.
  • WeightThreshold(threshold, mode="distance"|"similarity")
    Basic (or "naive") sparsification algorithm that simply applies a global weight threshold. Only edges with weight < threshold (distance) or > threshold (similarity) will be kept.
  • DoublyStochastic(tolerance=1e-5, max_iter=10000)
    Sinkhorn–Knopp alternating row/column normalization to make the adjacency (approximately) doubly stochastic without densifying (CSR-only). Can be useful as a normalization step before backboning/thresholding.
    Ref: Sinkhorn (1964); discussed in Coscia, "The Atlas for the Inspiring Network Scientist" (2025).
  • DisparityFilter(alpha=0.05, rule="or"|"and")
    Disparity Filter algorithm for graphs with continuous weights. Tests each edge against a node-wise null (Dirichlet/Beta split of strength). Undirected edges can be kept if either (“or”, default) or both (“and”) endpoints deem them significant.
    Ref: Serrano, Boguñá, Vespignani, "Extracting the multiscale backbone of complex weighted networks", PNAS 2009.
  • LocallyAdaptiveSparsification(alpha=0.05, rule="or"|"and")
    Implementation of the Locally Adaptive Network Sparsification (LANS) algorithm, which does not assume any particular null model. Instead, the distribution of similarity weights is used to determine and then retain statistically significant edges.
    Ref: Foti, Hughes, Rockmore, "Nonparametric Sparsification of Complex Multiscale Networks", 2011, https://doi.org/10.1371/journal.pone.0016431
  • MarginalLikelihoodFilter(alpha, float_scaling=20, assume_loopless=False)
    Dianati’s Marginal Likelihood Filter (MLF) for integer weights. Uses configuration-like binomial null preserving strengths on average; computes upper-tail p-values and keeps edges with ($p \le \alpha$). Supports float → integer casting strategies.
    Ref: Dianati, "Unwinding the hairball graph: Pruning algorithms for weighted complex networks", Phys. Rev. E 2016, https://link.aps.org/doi/10.1103/PhysRevE.93.012304
  • NoiseCorrected(delta=1.64, derivative="constant"|"full")
    Noise-Corrected (NC) backbone. Computes symmetric lift relative to a pairwise null, estimates variance via a binomial model with Beta prior (Bayesian shrinkage), and keeps edges exceeding ( $\delta$ ) standard deviations. derivative="full" matches the paper’s delta-method including ($d\kappa/dn$); "constant" is a simpler, fast variant.
    Ref: Coscia & Neffke, "Network Backboning with Noisy Data", 2017, https://ieeexplore.ieee.org/document/7929996

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Installation

pip install graphconstructor

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Quickstart

1) Build a graph (importers)

import numpy as np
from graphconstructor.importers import from_dense  # or use other options, e.g. from_knn, from_ann

# Symmetric distance matrix (example)
D = np.random.rand(100, 100) ** 0.5
D = (D + D.T) / 2
np.fill_diagonal(D, 0.0)

# Import (from dense array)
G0 = from_dense(D, directed=False)

2) Refine a graph (operators)

from graphconstructor.operators import KNNSelector, WeightThreshold

# Keep only the top-10 mutual neighbors (mutuality checked within top-20)
G_refined = KNNSelector(k=5, mutual=True, mutual_k=20, mode="distance").apply(G0)

# Prune weak edges (keep distance < 0.3)
G_pruned = WeightThreshold(threshold=0.3, mode="distance").apply(G_refined)

3) Export when needed

nx_graph = G_pruned.to_networkx()   # nx.Graph or nx.DiGraph
ig_graph = G_pruned.to_igraph()     # igraph.Graph