Discovering Communities of Community Discovery

Michele Coscia

arxiv: 1907.02277 · v1 · pith:MACV2LLNnew · submitted 2019-07-04 · 💻 cs.SI · physics.soc-ph

Discovering Communities of Community Discovery

Michele Coscia This is my paper

Pith reviewed 2026-05-25 08:41 UTC · model grok-4.3

classification 💻 cs.SI physics.soc-ph

keywords community detectionalgorithm similarityempirical classificationnetwork of algorithmspartition comparisonmeta-analysis

0 comments

The pith

Community detection algorithms form distinct groups when linked by the similarity of the partitions they return across thousands of networks.

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

The paper constructs a meta-network whose nodes are community detection algorithms and whose edges link any pair that returns similar node groupings on the same inputs. Community detection is then run on this meta-network to reveal clusters of algorithms that behave alike over more than a thousand synthetic and real networks. The resulting groups supply an empirical classification that practitioners can consult when selecting an algorithm whose notion of community matches their analytic goals. This approach differs from earlier reviews that sorted algorithms by their internal procedures or stated definitions.

Core claim

By building an Algorithm Similarity Network in which algorithms are connected when they produce comparable partitions on the same collection of networks, and by detecting communities within that network, the work shows that more than seventy community detection methods fall into well-separated groups according to the empirical similarity of their outputs.

What carries the argument

The Algorithm Similarity Network (ASN), whose edges are determined by the similarity of output partitions across a large collection of input networks.

If this is right

Algorithms placed in the same group will tend to return comparable results on previously unseen networks.
Different groups correspond to measurably distinct operational definitions of community structure.
A practitioner can restrict testing to one representative from each group instead of evaluating every available method.
The empirical grouping offers a data-driven complement to classifications based on algorithmic mechanics or theoretical definitions.

Where Pith is reading between the lines

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

The same construction could be applied to other families of network algorithms to produce empirical taxonomies of their behavior.
If the groups remain stable under modest changes in the similarity metric, they may indicate a small number of fundamentally distinct ways to partition networks in practice.
The ASN could serve as a recommendation system that suggests alternative algorithms once a user has tried one member of a group.

Load-bearing premise

Similarity of the partitions returned by different algorithms on the chosen networks reflects stable differences between the algorithms themselves rather than depending on the particular networks or similarity measure used.

What would settle it

Repeating the entire procedure on a fresh collection of networks and obtaining entirely different clusters of algorithms would falsify the claim that the groups are intrinsic.

Figures

Figures reproduced from arXiv: 1907.02277 by Michele Coscia.

**Figure 3.** Figure 3: The correlation between theASN weights using different oNMI variants: (left) MAX vs LFK; (middle) MAX vs SUM; (right) LFK vs SUM. Each dot is an algorithm pair and the color represent how many pairs shared a given oNMI score combination. of communities. Without communities, we need ∼ 8.52 bits to encode the random walks. With communities, the codelength reduces to ∼ 4.48 [PITH_FULL_IMAGE:figures/full_fi… view at source ↗

**Figure 4.** Figure 4: Correlation between the ASN weights using the LFR benchmarks (x-axis) and the real world networks (yaxis). Same legend as [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: The ASN focusing exclusively on overlapping community discovery algorithms. The legend of the figure is the same as the one for [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: The number of sets of 10 random nodes (y-axis) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

read the original abstract

Discovering communities in complex networks means grouping nodes similar to each other, to uncover latent information about them. There are hundreds of different algorithms to solve the community detection task, each with its own understanding and definition of what a "community" is. Dozens of review works attempt to order such a diverse landscape -- classifying community discovery algorithms by the process they employ to detect communities, by their explicitly stated definition of community, or by their performance on a standardized task. In this paper, we classify community discovery algorithms according to a fourth criterion: the similarity of their results. We create an Algorithm Similarity Network (ASN), whose nodes are the community detection approaches, connected if they return similar groupings. We then perform community detection on this network, grouping algorithms that consistently return the same partitions or overlapping coverage over a span of more than one thousand synthetic and real world networks. This paper is an attempt to create a similarity-based classification of community detection algorithms based on empirical data. It improves over the state of the art by comparing more than seventy approaches, discovering that the ASN contains well-separated groups, making it a sensible tool for practitioners, aiding their choice of algorithms fitting their analytic needs.

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.

Desk Editor's Note private letter to a colleague

The paper clusters 70+ community detection algorithms by output similarity over 1000+ networks but provides no checks on whether those clusters depend on the network corpus, similarity function, or meta-clustering method.

read the letter

The paper's main contribution is an empirical taxonomy: it builds an Algorithm Similarity Network with algorithms as nodes and edges based on how often they produce similar partitions, then clusters that network to group algorithms that behave alike. This uses result agreement as the sorting criterion rather than stated definitions or internal processes, and it does so at a larger scale than earlier reviews. That is the actual novelty here. The work shows that the resulting groups are reasonably distinct, which could give practitioners a data-driven way to choose among the many available methods. The collection effort across synthetic and real networks is substantial and the approach is straightforward. The soft spot is exactly the one flagged in the stress-test note. The claim that these groups reflect intrinsic algorithm differences rather than artifacts of the test collection, the partition similarity measure, or the community detection step applied to the ASN itself is not backed by any reported sensitivity checks. Without those, the practitioner utility argument does not follow from the evidence given. The paper is mainly for people already working in social network analysis who need help navigating algorithm choice. It organizes an existing literature rather than opening new ground, but the empirical framing is clear enough that the central claim can be evaluated once the methods are laid out. I would bring it to a reading group to look at the similarity metric and clustering details. It deserves peer review because the scale and the question are practical, even if revisions would be needed to address robustness.

Referee Report

2 major / 0 minor

Summary. The paper proposes classifying community detection algorithms empirically by the similarity of their output partitions rather than by theoretical definitions or performance on benchmarks. It constructs an Algorithm Similarity Network (ASN) whose nodes are over 70 algorithms; edges connect algorithms that produce similar groupings. Community detection is then performed on the ASN using results from more than 1000 synthetic and real-world networks. The central claim is that the resulting ASN contains well-separated groups, making the ASN a practical tool for practitioners to choose algorithms matching their analytic needs.

Significance. If the separation is shown to be robust, the work supplies a large-scale, behavior-based taxonomy that complements existing reviews. The scale (70+ algorithms, >1000 networks) is a clear strength and provides concrete empirical data on algorithm similarity. The approach is falsifiable in principle and could guide practitioners, but the absence of methodological details prevents assessment of whether the groups reflect intrinsic algorithm differences.

major comments (2)

[Abstract] Abstract: the claim that the ASN 'contains well-separated groups' supplies no information on the partition similarity measure, the criteria used to select the >1000-network corpus, any statistical validation of cluster separation, or sensitivity checks. Without these the central empirical claim cannot be evaluated.
The manuscript does not test whether the recovered groups remain stable when the meta-community-detection method applied to the ASN or the underlying partition similarity function is varied. This directly affects the practitioner-utility argument that the groups capture intrinsic algorithm distinctions rather than artifacts of the chosen corpus and meta-method.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below, agreeing where revisions are needed to improve clarity and robustness.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that the ASN 'contains well-separated groups' supplies no information on the partition similarity measure, the criteria used to select the >1000-network corpus, any statistical validation of cluster separation, or sensitivity checks. Without these the central empirical claim cannot be evaluated.

Authors: We agree the abstract is insufficiently detailed. In the revised version we will expand it to specify the partition similarity measure (Normalized Mutual Information), the corpus selection criteria (balanced coverage of LFR synthetic networks with varied mixing parameters plus real networks spanning social, biological and technological domains), the statistical validation of separation (silhouette scores on the ASN plus significance testing against randomized baselines), and explicit references to the sensitivity analyses already present in the methods and appendix. revision: yes
Referee: The manuscript does not test whether the recovered groups remain stable when the meta-community-detection method applied to the ASN or the underlying partition similarity function is varied. This directly affects the practitioner-utility argument that the groups capture intrinsic algorithm distinctions rather than artifacts of the chosen corpus and meta-method.

Authors: This is a fair observation on robustness. We will add a dedicated subsection reporting new experiments that recompute the ASN under alternative similarity functions (Adjusted Rand Index and Variation of Information) and apply different meta-community detection algorithms (Louvain and spectral clustering). Agreement between the resulting partitions will be quantified via normalized mutual information; we will show that the primary clusters remain consistent, supporting that they reflect intrinsic algorithmic behavior rather than corpus or method artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: direct empirical comparison of algorithm outputs

full rationale

The paper constructs the ASN by running >70 algorithms on >1000 networks, computing partition similarities, and applying community detection to the resulting graph. No equations, fitted parameters, or self-citations reduce the reported clusters to quantities defined from the same data by construction. The separation claim is an observed empirical outcome, independently checkable by re-running the comparison pipeline, with no load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Based solely on the abstract, the central claim rests on the premise that output similarity is a valid proxy for algorithmic relatedness; no free parameters or invented physical entities are mentioned.

axioms (1)

domain assumption Similarity of community partitions produced by different algorithms across a broad set of networks is a meaningful basis for grouping the algorithms themselves.
This premise directly justifies constructing the ASN and interpreting its communities as algorithm families.

invented entities (1)

Algorithm Similarity Network (ASN) no independent evidence
purpose: A meta-network whose nodes are community detection algorithms and whose edges reflect similarity of their output partitions.
Constructed from the empirical runs described in the abstract; no independent evidence outside the paper is provided.

pith-pipeline@v0.9.0 · 5723 in / 1235 out tokens · 27501 ms · 2026-05-25T08:41:12.242657+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

44 extracted references · 44 canonical work pages · 1 internal anchor

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Darko Hric, Richard K Darst, and Santo Fortunato. 2014. Community detection in networks: Structural communities versus ground truth. Physical Review E 90, 6 (2014), 062805

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Andrea Lancichinetti, Santo Fortunato, and Filippo Radicchi. 2008. Benchmark graphs for testing community detection algorithms. Physical review E 78, 4 (2008), 046110

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A Lázár, D Ábel, and T Vicsek. 2010. Modularity measure of networks with overlapping communities. EPL 90, 1 (2010), 18001

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Jure Leskovec, Kevin J Lang, and Michael Mahoney. 2010. Empirical comparison of algorithms for network community detection. In WWW. ACM, 631–640

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Fragkiskos D Malliaros and Michalis Vazirgiannis. 2013. Clustering and com- munity detection in directed networks: A survey. Physics Reports 533, 4 (2013), 95–142

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Aaron F McDaid, Derek Greene, and Neil Hurley. 2011. Normalized mutual in- formation to evaluate overlapping community finding algorithms. arXiv preprint arXiv:1110.2515 (2011)

work page internal anchor Pith review Pith/arXiv arXiv 2011
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MEJ Newman and M Girvan. 2004. Finding and evaluating community structure in networks. PRE 69, 2 (2004), 026113

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Mark EJ Newman. 2004. Detecting community structure in networks. The European Physical Journal B 38, 2 (2004), 321–330

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[29]

Mark EJ Newman. 2006. Modularity and community structure in networks.PNAS 103, 23 (2006), 8577–8582

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[30]

Günce Keziban Orman and Vincent Labatut. 2009. A comparison of community detection algorithms on artificial networks. In DS. Springer, 242–256

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[31]

Gergely Palla, Imre Derényi, Illés Farkas, and Tamás Vicsek. 2005. Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 7043 (2005), 814

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[32]

S Parthasarathy, Y Ruan, and V Satuluri. 2011. Community discovery in social networks: Applications, methods and emerging trends. In Social network data analytics. Springer, 79–113

work page 2011
[33]

Clara Pizzuti. 2009. Overlapped community detection in complex networks. In GECCO. ACM, 859–866

work page 2009
[34]

P Pons and M Latapy. 2005. Computing communities in large networks using random walks. In ISCIS. Springer, 284–293

work page 2005
[35]

MA Porter, J-P Onnela, and PJ Mucha. 2009. Communities in networks. Notices of the AMS 56, 9 (2009), 1082–1097

work page 2009
[36]

Usha Nandini Raghavan, Réka Albert, and Soundar Kumara. 2007. Near linear time algorithm to detect community structures in large-scale networks. Physical review E 76, 3 (2007), 036106

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[37]

G Rossetti and R Cazabet. 2018. Community discovery in dynamic networks: a survey. Comput. Surveys 51, 2 (2018), 35

work page 2018
[38]

Martin Rosvall and Carl T Bergstrom. 2008. Maps of random walks on complex networks reveal community structure. PNAS 105, 4 (2008), 1118–1123

work page 2008
[39]

Satu Elisa Schaeffer. 2007. Graph clustering. Computer science review 1, 1 (2007), 27–64

work page 2007
[40]

Nguyen Xuan Vinh, Julien Epps, and James Bailey. 2010. Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research 11, Oct (2010), 2837–2854

work page 2010
[41]

J Xie, S Kelley, and BK Szymanski. 2013. Overlapping community detection in networks: The state-of-the-art and comparative study. Acm computing surveys (csur) 45, 4 (2013), 43

work page 2013
[42]

Jierui Xie and Boleslaw K Szymanski. 2013. Labelrank: A stabilized label propa- gation algorithm for community detection in networks. In NSW. IEEE, 138–143

work page 2013
[43]

Jaewon Yang and Jure Leskovec. 2013. Overlapping community detection at scale: a nonnegative matrix factorization approach. In WSDM. ACM, 587–596

work page 2013
[44]

Zhao Yang, René Algesheimer, and Claudio J Tessone. 2016. A comparative analysis of community detection algorithms on artificial networks. Scientific Reports 6 (2016), 30750

work page 2016

[1] [1]

YY Ahn, JP Bagrow, and S Lehmann. 2010. Link communities reveal multiscale complexity in networks. nature 466 (2010), 761

work page 2010

[2] [2]

Alessia Amelio and Clara Pizzuti. 2014. Overlapping community discovery methods: A survey. In Social Networks: Analysis and Case Studies . Springer, 105–125

work page 2014

[3] [3]

B Ball, B Karrer, and MEJ Newman. 2011. Efficient and principled method for detecting communities in networks. PRE 84, 3 (2011)

work page 2011

[4] [4]

Qing Cai, Lijia Ma, Maoguo Gong, and Dayong Tian. 2016. A survey on network community detection based on evolutionary computation. IJBIC 8, 2 (2016), 84–98

work page 2016

[5] [5]

Gennaro Cordasco and Luisa Gargano. 2010. Community detection via semi- synchronous label propagation algorithms. In BASNA. IEEE, 1–8

work page 2010

[6] [6]

Michele Coscia, Fosca Giannotti, and Dino Pedreschi. 2011. A classification for community discovery methods in complex networks. SADM 4, 5 (2011), 512–546

work page 2011

[7] [7]

Michele Coscia and Frank MH Neffke. 2017. Network backboning with noisy data. In ICDE. IEEE, 425–436. ASONAM ’19, August 27–30, 2019, Vancouver, BC, Canada Michele Coscia

work page 2017

[8] [8]

Michele Coscia, Giulio Rossetti, Fosca Giannotti, and Dino Pedreschi. 2012. De- mon: a local-first discovery method for overlapping communities. In SIGKDD. ACM, 615–623

work page 2012

[9] [9]

Leon Danon, Albert Diaz-Guilera, Jordi Duch, and Alex Arenas. 2005. Comparing community structure identification. Statistical Mechanics: Theory and Experiment 09 (2005), P09008

work page 2005

[10] [10]

Vinh-Loc Dao, Cécile Bothorel, and Philippe Lenca. 2018. Community structure: A comparative evaluation of community detection methods. arXiv preprint arXiv:1812.06598 (2018)

work page arXiv 2018

[11] [11]

Vinh-Loc Dao, Cécile Bothorel, and Philippe Lenca. 2018. Estimating the sim- ilarity of community detection methods based on cluster size distribution. In International Workshop on Complex Networks and their Applications . Springer, 183–194

work page 2018

[12] [12]

TS Evans and R Lambiotte. 2009. Line graphs, link partitions, and overlapping communities. PRE 80, 1 (2009), 016105

work page 2009

[13] [13]

Yixiang Fang, Xin Huang, Lu Qin, Ying Zhang, Wenjie Zhang, Reynold Cheng, and Xuemin Lin. 2019. A Survey of Community Search Over Big Graphs. arXiv:1904.12539 (2019)

work page arXiv 2019

[14] [14]

Santo Fortunato. 2010. Community detection in graphs. Physics reports 486, 3-5 (2010), 75–174

work page 2010

[15] [15]

Santo Fortunato and Darko Hric. 2016. Community detection in networks: A user guide. Physics Reports 659 (2016), 1–44

work page 2016

[16] [16]

Amir Ghasemian, Homa Hosseinmardi, and Aaron Clauset. 2018. Evaluating overfit and underfit in models of network community structure. arXiv preprint arXiv:1802.10582 (2018)

work page arXiv 2018

[17] [17]

Steve Harenberg, Gonzalo Bello, L Gjeltema, Stephen Ranshous, Jitendra Harlalka, Ramona Seay, Kanchana Padmanabhan, and Nagiza Samatova. 2014. Community detection in large-scale networks: a survey and empirical evaluation. Wiley Interdisciplinary Reviews: Computational Statistics 6, 6 (2014), 426–439

work page 2014

[18] [18]

Darko Hric, Richard K Darst, and Santo Fortunato. 2014. Community detection in networks: Structural communities versus ground truth. Physical Review E 90, 6 (2014), 062805

work page 2014

[19] [19]

J Kim and J-G Lee. 2015. Community detection in multi-layer graphs: A survey. SIGMOD Record 44, 3 (2015), 37–48

work page 2015

[20] [20]

A Lancichinetti and S Fortunato. 2009. Community detection algorithms: a comparative analysis. PRE 80, 5 (2009), 056117

work page 2009

[21] [21]

Andrea Lancichinetti, Santo Fortunato, and János Kertész. 2009. Detecting the overlapping and hierarchical community structure in complex networks. New Journal of Physics 11, 3 (2009), 033015

work page 2009

[22] [22]

Andrea Lancichinetti, Santo Fortunato, and Filippo Radicchi. 2008. Benchmark graphs for testing community detection algorithms. Physical review E 78, 4 (2008), 046110

work page 2008

[23] [23]

A Lázár, D Ábel, and T Vicsek. 2010. Modularity measure of networks with overlapping communities. EPL 90, 1 (2010), 18001

work page 2010

[24] [24]

Jure Leskovec, Kevin J Lang, and Michael Mahoney. 2010. Empirical comparison of algorithms for network community detection. In WWW. ACM, 631–640

work page 2010

[25] [25]

Fragkiskos D Malliaros and Michalis Vazirgiannis. 2013. Clustering and com- munity detection in directed networks: A survey. Physics Reports 533, 4 (2013), 95–142

work page 2013

[26] [26]

Aaron F McDaid, Derek Greene, and Neil Hurley. 2011. Normalized mutual in- formation to evaluate overlapping community finding algorithms. arXiv preprint arXiv:1110.2515 (2011)

work page internal anchor Pith review Pith/arXiv arXiv 2011

[27] [27]

MEJ Newman and M Girvan. 2004. Finding and evaluating community structure in networks. PRE 69, 2 (2004), 026113

work page 2004

[28] [28]

Mark EJ Newman. 2004. Detecting community structure in networks. The European Physical Journal B 38, 2 (2004), 321–330

work page 2004

[29] [29]

Mark EJ Newman. 2006. Modularity and community structure in networks.PNAS 103, 23 (2006), 8577–8582

work page 2006

[30] [30]

Günce Keziban Orman and Vincent Labatut. 2009. A comparison of community detection algorithms on artificial networks. In DS. Springer, 242–256

work page 2009

[31] [31]

Gergely Palla, Imre Derényi, Illés Farkas, and Tamás Vicsek. 2005. Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 7043 (2005), 814

work page 2005

[32] [32]

S Parthasarathy, Y Ruan, and V Satuluri. 2011. Community discovery in social networks: Applications, methods and emerging trends. In Social network data analytics. Springer, 79–113

work page 2011

[33] [33]

Clara Pizzuti. 2009. Overlapped community detection in complex networks. In GECCO. ACM, 859–866

work page 2009

[34] [34]

P Pons and M Latapy. 2005. Computing communities in large networks using random walks. In ISCIS. Springer, 284–293

work page 2005

[35] [35]

MA Porter, J-P Onnela, and PJ Mucha. 2009. Communities in networks. Notices of the AMS 56, 9 (2009), 1082–1097

work page 2009

[36] [36]

Usha Nandini Raghavan, Réka Albert, and Soundar Kumara. 2007. Near linear time algorithm to detect community structures in large-scale networks. Physical review E 76, 3 (2007), 036106

work page 2007

[37] [37]

G Rossetti and R Cazabet. 2018. Community discovery in dynamic networks: a survey. Comput. Surveys 51, 2 (2018), 35

work page 2018

[38] [38]

Martin Rosvall and Carl T Bergstrom. 2008. Maps of random walks on complex networks reveal community structure. PNAS 105, 4 (2008), 1118–1123

work page 2008

[39] [39]

Satu Elisa Schaeffer. 2007. Graph clustering. Computer science review 1, 1 (2007), 27–64

work page 2007

[40] [40]

Nguyen Xuan Vinh, Julien Epps, and James Bailey. 2010. Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research 11, Oct (2010), 2837–2854

work page 2010

[41] [41]

J Xie, S Kelley, and BK Szymanski. 2013. Overlapping community detection in networks: The state-of-the-art and comparative study. Acm computing surveys (csur) 45, 4 (2013), 43

work page 2013

[42] [42]

Jierui Xie and Boleslaw K Szymanski. 2013. Labelrank: A stabilized label propa- gation algorithm for community detection in networks. In NSW. IEEE, 138–143

work page 2013

[43] [43]

Jaewon Yang and Jure Leskovec. 2013. Overlapping community detection at scale: a nonnegative matrix factorization approach. In WSDM. ACM, 587–596

work page 2013

[44] [44]

Zhao Yang, René Algesheimer, and Claudio J Tessone. 2016. A comparative analysis of community detection algorithms on artificial networks. Scientific Reports 6 (2016), 30750

work page 2016