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arxiv: 1906.12332 · v1 · pith:U6RZ3RDQnew · submitted 2019-06-26 · 💻 cs.SI · cs.LG· cs.NE

Automatic Discovery of Families of Network Generative Processes

Telmo Menezes (CMB) , Camille Roth (CMB) This is my paper

Pith reviewed 2026-05-25 15:07 UTC · model grok-4.3

classification 💻 cs.SI cs.LGcs.NE
keywords network generative modelssymbolic regressiongenetic programmingsocial networksFacebook ego networksnetwork familiesgenotypephenotype
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The pith

Symbolic regression groups networks by their inferred generative processes rather than observed statistical features.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews how symbolic regression through genetic programming can automatically discover the functions driving network formation, moving beyond the need for scholars to guess key drivers in advance. It then shows that this method can identify families of networks sharing similar generative rules, which the authors term genotypes, allowing classification independent of surface traits like degree sequences or clustering. The demonstration uses an original collection of 238 anonymized Facebook ego-centered friendship networks to illustrate the approach and extract formation insights for sociability networks. A reader would care because the technique offers a data-driven route to model building that could unify understanding across seemingly different networks. If the grouping holds, models of network evolution become more portable between datasets without re-deriving intuitions each time.

Core claim

The paper establishes that symbolic regression recovers families of networks describable by similar generative processes, so that networks may be grouped according to their inferred genotype in terms of generative processes rather than their observed phenotype in terms of statistical or topological features. This is shown by applying the method to the Facebook ego-network dataset, yielding concrete groupings and formation insights.

What carries the argument

Symbolic regression via genetic programming, which evolves fundamental network dynamic functions to infer generative processes and thereby group networks by shared genotype.

If this is right

  • Networks become classifiable into families based on shared generative rules recovered from data.
  • Design of network models can proceed with less reliance on a priori intuitions about formation drivers.
  • Insights into sociability network formation emerge directly from the Facebook ego-network groupings.
  • The artificial-scientist approach extends to automatic discovery of network evolution processes.
  • Phenotype-based clustering of networks can be supplemented or replaced by genotype-based clustering.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same method could be tested on non-social networks such as citation or biological interaction graphs to check whether generative families appear across domains.
  • If genotypes prove stable over time, the approach might support short-term prediction of how an observed network will continue to grow.
  • Cross-dataset comparison of recovered genotypes could identify whether certain generative rules recur universally.

Load-bearing premise

The genetic programming procedure recovers meaningful generative processes rather than spurious expressions that merely fit the observed networks.

What would settle it

Finding multiple unrelated generative expressions that fit the same Facebook networks equally well, with no independent criterion to decide which expressions capture actual formation mechanisms.

Figures

Figures reproduced from arXiv: 1906.12332 by Camille Roth (CMB), Telmo Menezes (CMB).

Figure 1
Figure 1. Figure 1: This unconventional antenna design was generated by NASA using evolutionary computa [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Evolutionary loop including the synthetic network generation process. The outer part of [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Network generators mapped into a two-dimensional layout according to their pairwise dis [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Top panel, and bottom-left: Boxplots of numbers of nodes, edges and densities for the underlying networks of the various families, as well as all, unclassified and classified. Horizontal dashed line indicates overall median. Bottom-right: Stacked plot of family ratio per percentile of network density. understanding, we created boxplots of the distributions of node and edge counts for the underlying network… view at source ↗
Figure 5
Figure 5. Figure 5: Boxplots of best fitnesses achieved (lower is better) for the underlying networks of the [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
read the original abstract

Designing plausible network models typically requires scholars to form a priori intuitions on the key drivers of network formation. Oftentimes, these intuitions are supported by the statistical estimation of a selection of network evolution processes which will form the basis of the model to be developed. Machine learning techniques have lately been introduced to assist the automatic discovery of generative models. These approaches may more broadly be described as "symbolic regression", where fundamental network dynamic functions, rather than just parameters, are evolved through genetic programming. This chapter first aims at reviewing the principles, efforts and the emerging literature in this direction, which is very much aligned with the idea of creating artificial scientists. Our contribution then aims more specifically at building upon an approach recently developed by us [Menezes \& Roth, 2014] in order to demonstrate the existence of families of networks that may be described by similar generative processes. In other words, symbolic regression may be used to group networks according to their inferred genotype (in terms of generative processes) rather than their observed phenotype (in terms of statistical/topological features). Our empirical case is based on an original data set of 238 anonymized ego-centered networks of Facebook friends, further yielding insights on the formation of sociability networks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper reviews the use of symbolic regression via genetic programming for automatic discovery of network generative models, building on the authors' 2014 work. It then applies the approach to an original dataset of 238 anonymized Facebook ego networks to demonstrate that networks can be grouped into families sharing similar inferred generative processes (genotype) rather than similar topological or statistical features (phenotype).

Significance. If the recovered expressions can be shown to correspond to actual generative mechanisms that produce the observed networks, the work would provide a data-driven alternative to a priori model specification in network science and support the broader program of automated scientific discovery. The distinction between genotype-based and phenotype-based grouping is conceptually interesting for sociability networks, but the manuscript provides no ground-truth validation to establish that the expressions are generative rather than post-hoc statistical fits.

major comments (2)
  1. [Results / Empirical case study] The central claim that symbolic regression recovers meaningful generative processes (rather than flexible expressions fitting observed statistics) lacks supporting validation. No experiments are described that test recovery of known generators on synthetic networks, nor are alternative expressions that yield equivalent statistics shown to be rejected. This is load-bearing for the genotype/phenotype distinction and the family-discovery result.
  2. [Introduction / Contribution statement] The family grouping rests on quantities defined by the 2014 Menezes & Roth procedure. It is unclear whether the 238-network analysis supplies independent evidence that the discovered families reflect shared generative rules rather than shared statistical signatures already captured by the earlier fitted model.
minor comments (1)
  1. [Abstract] The abstract states that the method 'demonstrate[s] the existence of families' but provides no quantitative measure (e.g., within-family vs. between-family distance on the discovered expressions) to support the grouping claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below, indicating where revisions will be made to clarify the manuscript's contributions and limitations.

read point-by-point responses

  1. Referee: [Results / Empirical case study] The central claim that symbolic regression recovers meaningful generative processes (rather than flexible expressions fitting observed statistics) lacks supporting validation. No experiments are described that test recovery of known generators on synthetic networks, nor are alternative expressions that yield equivalent statistics shown to be rejected. This is load-bearing for the genotype/phenotype distinction and the family-discovery result.

    Authors: The validation experiments demonstrating recovery of known generators on synthetic networks were reported in our 2014 Menezes & Roth paper that introduced the method. The present manuscript applies that established procedure to a new collection of 238 real Facebook ego networks, with the primary contribution being the demonstration that genotype-based grouping yields families distinct from phenotype-based groupings. We agree that the manuscript would benefit from more explicit cross-referencing to the prior validation results and a clearer statement that the current work does not repeat synthetic recovery tests. We will revise the results and discussion sections accordingly. revision: partial

  2. Referee: [Introduction / Contribution statement] The family grouping rests on quantities defined by the 2014 Menezes & Roth procedure. It is unclear whether the 238-network analysis supplies independent evidence that the discovered families reflect shared generative rules rather than shared statistical signatures already captured by the earlier fitted model.

    Authors: The 238 ego networks constitute an original dataset collected for this study and were not analyzed in the 2014 work. Applying the procedure to these networks produces inferred generative expressions whose similarity structure is then used for clustering; we show that the resulting families differ from those obtained by clustering on standard topological statistics. This supplies empirical evidence that the genotype-based grouping captures structure beyond the statistical signatures used in the earlier model. We will revise the introduction to state this distinction more explicitly and to highlight the novelty of the Facebook dataset. revision: yes

Circularity Check

0 steps flagged

No circularity detected; empirical application of prior method to new dataset

full rationale

The paper applies the authors' 2014 symbolic regression procedure to a fresh dataset of 238 Facebook ego networks, evolving expressions per network and then grouping by similarity of those expressions. This constitutes an empirical demonstration rather than a derivation that reduces to its own inputs by construction. The self-citation identifies the method being reused but does not make the central claim (existence of families in this specific data) equivalent to the method definition itself. No equations or steps in the provided text exhibit self-definition, fitted inputs renamed as predictions, or load-bearing uniqueness imported solely from overlapping-author citations. The analysis remains self-contained against the external 238-network benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The approach implicitly assumes genetic programming can search the space of network evolution functions effectively.

axioms (1)
  • domain assumption Genetic programming can evolve network dynamic functions that correspond to real generative processes.
    Central to the symbolic regression pipeline described in the abstract.

pith-pipeline@v0.9.0 · 5754 in / 1153 out tokens · 27028 ms · 2026-05-25T15:07:56.188298+00:00 · methodology

discussion (0)

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