Roadmap#

This page tracks where nx-backbone is headed: what was finished recently, known gaps against the cited methods, and planned features. It consolidates the design notes in docs/design/ (the Backbone 3.0 coverage evaluation, the Yassin et al. (2025) coverage evaluation, the hypergraph backboning proposal, the generalized null distributions report, and the temporal backbones proposal). Each open item links to its GitHub issue; #31 tracks them all. Contributions are welcome. Please comment on an issue before starting one of the larger items.

Status key: done, next (planned for the next release), planned, idea (open for discussion).

Roadmap at a glance#

These figures and the table below are generated from this page every time the documentation is built, so they always match the lists that follow.

Horizontal stacked bar chart of roadmap items per section, split by status (idea, planned, next, done). — Roadmap items per section, by status.#

Network diagram: each roadmap section is a gray hub connected to its items, which are colored by status and labeled with their GitHub issue numbers. — Each section (gray) and its items, colored by status and labeled with their GitHub issue numbers.#

Roadmap items by section and status#
Section	Idea	Planned	Done	Total
Recently completed: Method coverage	0	0	2	2
Next release (0.3.0): Correctness gaps found in review	0	0	10	10
Next release (0.3.0): Validation	0	0	3	3
Next release (0.3.0): Documentation, tutorials, and figures	0	0	8	8
Next release (0.3.0): Release engineering	0	0	2	2
Planned features: API and ecosystem compatibility	0	0	5	5
Planned features: Methods	1	1	11	13
Planned features: Temporal backbones	4	1	5	10
Planned features: Documentation	0	0	3	3
All sections	5	2	49	56

Recently completed#

Method coverage#

done: Every backbone model in Neal’s Backbone 3.0 R package, plus its cross-cutting features: multiple-testing correction (mtc), signed backbones, and SDSM-EC edge constraints.
done: Hypergraph backbones: the MDL backbone (Kirkley et al., 2026), statistically validated hypergraphs and cores (SVH/SVC), structural reductions, and HIF/xgi/HyperNetX/HypergraphX/HAT interoperability.

Correctness review (2026-11)#

A full code review checked each method against its paper. The fixes below change numerical results, so they are listed in the Changelog as breaking changes:

ecm_filter: the solver did not converge and every p-value was about 0. It is now a maximum-likelihood fit with a Newton polish, using the geometric tail \(p_{ij}(y_iy_j)^{w-1}\).
marginal_likelihood_filter: now Dianati’s null model \(B(T, s_is_j/2T^2)\). The old one was asymmetric and depended on the order nodes were added.
glab_filter: now uses per-node shortest-path involvement and \((1-I_{ij})^{(k_i-1)^c}\) (Zhang et al., 2014) instead of global edge betweenness.
disparity_filter on directed graphs: now also tests the target’s incoming links (Serrano et al., 2009).
Bipartite: the FDSM null now preserves degrees (a curveball chain with burn-in, and p-values of (count + 1) / (trials + 1)). The BiCM is fitted exactly, with exact or RNA Poisson-binomial tails. SDSM-EC refits on the free cells. fixedfill and fixedcol use their exact null distributions. backbone_from_projection thresholds every method at alpha.
See the Changelog for the full bipartite, hypergraph, and structural lists.
Shared conventions: every scorer rejects multigraphs, rejects NaN or infinite weights, works with node labels of mixed types, and preserves graph, node, and edge attributes through the filters.
CI now runs tests on every push and pull request (Python 3.12-3.14 and a NetworkX-only job), along with ruff lint and format checks and doctests.

Next release (0.3.0)#

Correctness gaps found in review#

done (#9): noise_corrected_filter is a binomial z-score. Implement the full Bayesian noise-corrected backbone of Coscia & Neffke (2017): the posterior variance from the beta prior plus the delta method, and the transformed lift score. Keep the current score as an option for backward compatibility.
done (#10): The dominance-fitting multiple linkage analysis is implemented (method="dominance"). Its fit is the coefficient of determination, checked against Table 1 of Van Nuffel, Derudder & Witlox (2010); the whole-profile sum of squares and Weaver’s variance are available through deviation=. The 2007 paper itself is paywalled and was not read.
done (#11, contributed in #34): Directed lans_filter now also tests the target’s in-links.
done (#12): A directed GLAB variant, using the out- and in-involvement of Zhang et al. (2014), Section 2.3.
done (#13): Check hyper_projection’s weighting (\(1/d(z)\) versus Newman’s \(1/(d(z)-1)\)) and the arXiv identifier cited for the projection methods against Coscia & Neffke (2017).
done (#58): The signed lans_filter lower tail is now #{weights < w} / k, the mirror image of the upper tail, as in R. Its two-sided p-values equal R’s, and since #59 so do the signs of exact ties. Les Misérables: 0 -> 126 negative links, as in R (40 of them ties).
done (#60): strongest_n_ties keeps edges tied at each node’s cutoff together, so G, G.copy(), and any reordering of the same graph give the same backbone. global_sparsification and edge_betweenness_filter no longer depend on edge orientation. planar_maximally_filtered_graph and maximum_spanning_tree_backbone (ties in weight), fraction_filter (ties in score, documented), and modularity_backbone (Louvain visiting order, even with a fixed seed) still depend on input order.
done (#59): Decide, for each convention difference from R backbone and netbone that the reference tests document, whether to keep it, match the reference, or add an option. The decision note measures each difference on the reference datasets and records the decisions: every difference is kept and documented, except the sign of an exact tie between the two tails, which now matches R (-1), so every signed weighted backbone equals R’s on the fixtures. R-compatible options are available without changing any default: backbone_from_projection(missing_as_zero=False) and lspar(convention="r").
done (#105): noise_corrected_filter’s p-values were far too small on low-count graphs (pure-noise edges at p ≈ 1e-66), because the paper’s delta rule is not a calibrated test. nc_pvalue is now the exact binomial tail of the method’s null model (the paper’s footnote 2), checked by simulation; the delta rule’s p-value is pvalue_method="delta". Les Misérables: 195 -> 126 edges.
done (#108): sdsm(pvalue_method="auto") computes exact Poisson-binomial tails whenever that is affordable, instead of the refined normal approximation above 200 artifacts, whose far upper tail let pure-noise pairs pass a BH correction on sparse data. Truncated convolutions make the exact tails 8-60x cheaper; over budget, the pairs with the smallest expected co-occurrence keep exact tails and a warning names the rest. pvalue_method="rna" still matches R backbone.

Validation#

done (#14): Cross-implementation reference tests. P-values and backbones on Les Misérables, Davis Southern Women, and karate are pinned against R backbone 3.0.4 and netbone 0.2.3 in JSON fixtures, so the test suite needs neither R nor netbone.
done (#15): An optional “Interop” CI workflow that installs xgi, HyperNetX, HypergraphX, and HAT (the [interop] extra) and runs the adapter and HIF round-trip tests against the real libraries on pull requests and weekly. Supported versions are listed in Installation.
done (#17): Turn on numpydoc validation (numpydoc_validation_checks) in the docs build so missing Parameters, Returns, or Examples sections fail CI.

Documentation, tutorials, and figures#

Longer, narrative documentation with figures, tracked in #96. Each tutorial is executed when the docs are built, so its numbers and figures cannot drift from the code, and uses one colorblind-safe figure style.

done (#88): Regenerate and redesign the per-method gallery on the API pages, whose images dated from 0.2.0 and showed pre-fix results, and generate it at build time so it cannot go stale. Every figure uses the shared figure style (docs/_figures/style.py) that the examples and tutorials also use.
done (#89): Narrative tutorial: from a hairball to a backbone, end to end (why a backbone, scoring vs filtering, choosing alpha and corrections, comparing, validating, reporting), the “Start here” entry point of the tutorials.
done (#90): Narrative tutorial: the statistical null models side by side, including generalized nulls and signed backbones.
done (#91): Narrative tutorial: structural and proximity backbones, and when topology-based guarantees beat significance tests.
done (#92): Narrative tutorial: bipartite projections and their backbones.
done (#93): Narrative tutorial: hypergraph backbones (groups versus pairs, the MDL and local MDL backbones, SVH and SVC, the structural helpers, and HIF interchange), executed with six figures.
done (#94): Narrative tutorial: temporal backbones, from snapshots to smoothing.
done (#95): Narrative guides: coming from R backbone or netbone, and scaling up to large networks.

Release engineering#

done (#16): Release v0.3.0, the first release with this sprint’s correctness fixes, new methods, and changes in results, and the first as nx-backbone (#119). Released 2026-11-02 to PyPI from the tag-checked workflow (v0.2.0 never reached PyPI: its tag still had a static version = "0.1.0"). The anaconda.org package is still to come: the conda build failed before building (conda-verify has no Python 3.12 build).
done (#18): Add py.typed and type annotations for the public API, checked by a non-strict mypy CI job.

Planned features#

API and ecosystem compatibility#

done (#19): NetworkX backend dispatching (@nx._dispatchable) so backends such as nx-cugraph and nx-parallel can accelerate the shortest-path-heavy methods (salience, metric backbone, GLAB). The graph-in, graph-out functions dispatch as backbone_*, the tests pass under NETWORKX_TEST_BACKEND=nx_loopback, and Backends records nx-parallel timings.
done (#20): Accept SciPy sparse arrays and pandas edge lists as input: bipartite functions take incidence matrices, and backbone, backbone_from_weighted and backbone_from_unweighted take adjacency matrices and edge lists via to_graph(), matching how NetworkX interoperates with the NumPy/SciPy/pandas stack.
done (#30): Make the bipartite and projection code fully sparse (no dense agent-by-artifact matrices). The per-pair loops are already vectorized.
done (#21): A sparse or blockwise ECM solver for graphs with more than about 2,000 nodes. The fit now runs over degree-strength classes with chunked pair sums and Newton or Newton-CG steps.
done (#22): An asv benchmark suite, so performance regressions show up in review.

Methods#

done (#23): describe_backbone (Backbone 3.0’s narrative): methods text and citations for a chosen backbone and its parameters.
done (#32): sparsify(umst=True) should add the union of all minimum spanning trees (Hamann et al., 2016), not a single spanning forest.
done (#24): The local (per-node-neighborhood) MDL hypergraph backbone (Kirkley et al., 2026, Appendix E): local_mdl_hypergraph_backbone.
done (#25): Signed variants of ecm_filter and the noise-corrected filter, for parity with the other scorers’ signed=True.
done (#26): A missing_as_zero toggle for weighted inputs (Backbone 3.0), for testing absent dyads.
done (#29): Survey the methods in the Yassin et al. (2025) statistical and structural comparisons. With #42-#44 the package covers all 15 methods; see the coverage table.
done (#42): The Pólya urn filter (Marcaccioli & Livan, 2019), missing per the #29 survey, as polya_filter(). Its null model is unlike any method here, and Yassin et al. (2025) found it best preserves the weight distribution.
done (#43): The GloSS filter (Radicchi et al., 2011), missing per the #29 survey: gloss_filter(), a global null with weights drawn from the observed weight distribution over the fixed topology.
done (#44): The connectivity stage of Slater’s (2009) doubly stochastic backbone (add edges by ds_weight until the backbone is connected), the variant Yassin et al. (2025) evaluate. doubly_stochastic_filter now flags it as ds_keep.
done (#54): doubly_stochastic_filter(smoothing=...) adds a pseudocount so Sinkhorn-Knopp converges on sparse graphs, and ds_weight no longer depends on node insertion order when it does not converge.
done (#55): Relax the distributional assumptions of the statistical nulls: a transform_weights preprocessing helper with an invariance table, a generalized disparity_filter(a=...) share null with a calibration test harness, and an explicit count unit= for MLF, ECM, and the noise-corrected filter. Not scheduled: a continuous-weight ECM, an overdispersed MLF, and user-supplied weight distributions for GloSS.
planned (#76): fdsm Monte Carlo resolution diagnostics: warn when 1/(trials+1) makes family-wise significance unreachable, and report the p-value’s Monte Carlo uncertainty.
idea (#77): fdsm(refine="splitting"): adaptive multilevel splitting for p-values below the Monte Carlo floor.

Temporal backbones#

A new top-level module, nx_backbone.temporal, for filtering networks observed over time. It accepts snapshots (a list or dict of graphs), timestamped events, and time spans equally, bins events and spans into steps, and returns one scored static graph, so the usual filters apply. The design and the method proposals are in the temporal backbones proposal; #78 tracks the work.

done (#67): Foundation: the three input forms, binning with freq=, the node-presence rule (an absent edge is zero only when both endpoints are present), and the scored-static-graph output: temporal_form, lossless conversions between the forms, flatten_temporal, the shared presence and eligibility masks, and the API-contract kind="temporal".
done (#68): observation_fraction and persistence (runs of consecutive observed steps).
done (#69): backbone_stability (how often any static scorer keeps an edge across steps) and weight_trend.
planned (#70): Interop with pandas event tables, DyNetX, teneto, and pathpy. Done so far: pandas event tables (from_event_table, to_event_table). Remaining: the DyNetX, teneto, and pathpy adapters.
idea (#71): Null-model significance tests for the simple filters.
done (#72): kalman_backbone: Kalman smoothing of per-step edge significance, tested against an exact null, with an edge-level test across steps and kalman_snapshots for per-step graphs.
done (#73): edge_persistence_hmm: a two-state hidden Markov model for persistent edge activity, observing presence, per-step keep flags, or p-values.
idea (#112): Edge classes or a mixture over edges for edge_persistence_hmm, so that persistent and flickering edges need not share one chain. Done for 0.3.0: Notes on the trade-off between miss rate and switching rate, and an unobserved_active_share diagnostic in the fitted record; a Beta prior on the error rates (MAP-EM) was evaluated and not adopted.
idea (#74): wavelet_denoise: wavelet shrinkage of edge-weight time series before backboning.
idea (#75): poisson_lift_filter: a Gamma-Poisson state-space filter for count weights.

Documentation#

done (#27): A “validating a backbone” tutorial showing the compare_backbones, consensus_backbone, and mtc workflow end to end.
done (#28): Turn the Les Misérables benchmark table into an executed Sphinx-Gallery example, so its edge counts cannot go stale.
done (#56): Generate the “Roadmap at a glance” figures and table on this page from the roadmap itself on every docs build.