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arxiv: 2306.07927 · v3 · submitted 2023-06-02 · 💻 cs.SI

A Survey of Densest Subgraph Discovery on Large Graphs

Wensheng Luo , Chenhao Ma , Yixiang Fang , Laks V.S. Lakshmanan This is my paper

Pith reviewed 2026-05-24 08:17 UTC · model grok-4.3

classification 💻 cs.SI
keywords densest subgraph discoverygraph mininglarge graphssurveysocial networksapplicationsfuture directions
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The pith

Densest subgraph discovery methods on large graphs can be classified into several groups for systematic review and comparison across roughly 50 papers.

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

The paper surveys the densest subgraph discovery problem, noting its use in spotting filter bubbles, misinformation spreaders, communities in social networks, and regulatory motifs in DNA. It first lays out the practical importance and computational challenges of the task, then organizes existing solutions into categories that together cover about 50 papers from venues such as SIGMOD, PVLDB, TODS, and WWW. Within each category the survey reviews the methods, compares their models, and closes by naming open research directions. A reader would care because the classification turns a scattered body of work into a single map that lets practitioners pick suitable techniques for their graphs and lets researchers see what remains unexplored.

Core claim

This survey first highlights the importance of densest subgraph discovery in real-world applications and the challenges involved, then classifies existing solutions into several groups covering around 50 papers, reviews the solutions in each group, analyzes and compares the models, and identifies promising future research directions.

What carries the argument

The classification of DSD solutions into several groups that organizes the literature for review, comparison, and identification of future directions.

If this is right

  • Researchers obtain a clearer map of existing densest subgraph models and can select methods appropriate to graph size and application.
  • Connections between DSD and related problems such as network flow become easier to exploit when the reviewed solutions are compared side by side.
  • Identified future directions supply concrete starting points for new work in the database, data mining, and network communities.
  • Practitioners gain guidance on which algorithms handle the scale and constraints of their specific graphs.

Where Pith is reading between the lines

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

  • The survey's grouping may highlight under-explored areas such as dynamic or streaming graphs where new methods could be developed.
  • Links between DSD and community detection suggest hybrid algorithms that combine ideas from both areas but are not yet covered.
  • Testing the classification against papers published after the survey would reveal whether the groups remain stable or need expansion.

Load-bearing premise

The selected set of approximately 50 papers and the chosen grouping into categories provide a representative and non-overlapping coverage of the DSD literature without major omissions or misclassifications of key methods.

What would settle it

The discovery of one or more substantial DSD papers published in SIGMOD, PVLDB, TODS, or WWW that fit none of the survey's groups or were omitted would show the classification is incomplete.

Figures

Figures reproduced from arXiv: 2306.07927 by Chenhao Ma, Laks V.S. Lakshmanan, Wensheng Luo, Yixiang Fang.

Figure 1
Figure 1. Figure 1: Examples of undirected and directed graphs. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An undirected Graph G and its flow network F. (2) Charikar [33] proposed to transfer the original UDS problem as a linear programming (LP) problem and developed an exact algorithm. Given a vertex set S ⊆ V , let E(S) be the edge set induced by S, i.e., E(S) = {u, v ∈ S, uv ∈ E}. Let xv and ye be the vari￾ables assigned to the edge e and vertex v, respectively, where xv = 1/|S| indicates that v is included … view at source ↗
Figure 3
Figure 3. Figure 3: An example of the core-based algorithm. For example, for the graph in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: An undirected Graph G and its flow network where Ψ is a triangle. imum number of triangles in the graph and retuen the subgraph with the largest triangle density. Fang et al. [54] proposed the concept of (k, Ψ)-core based on k-core. Given an integer k and an h-clique Ψ, all vertices in (k, Ψ)-core are contained by at least k instances of Ψ. Based on (k, Ψ)-core, CoreExact and CoreApp can provide exact and … view at source ↗
Figure 5
Figure 5. Figure 5: Flow network built for the graph in Fig. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Examples of [x, y]-cores [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Duplicating vertices to two copies. of the max-flow computation. Later, Ma et al. [108] extended the [x, y]-core concept to weighted directed graphs and proposed efficient weighted DDS algorithms based on the weighted [x, y]-cores. 4.2 Approximation algorithms The approximation DDS algorithms can also be cate￾gorized into different groups according to the main tech￾niques used: 1. peeling-based algorithms … view at source ↗
Figure 9
Figure 9. Figure 9: Relationship of various density definitions. graphs, since edges have the probability of existence, edge-density is extended to expected density, which is the ratio of the sum of the probabilities of all edges of the graph to the number of vertices. For uncertain graphs with uncertain edge weights, robust ratio is pro￾posed to evaluate the robustness of subgraphs. 6.2 Comparison of DSD solutions As reviewe… view at source ↗
read the original abstract

With the prevalence of graphs for modeling complex relationships among objects, the topic of graph mining has attracted a great deal of attention from both academic and industrial communities in recent years. As one of the most fundamental problems in graph mining, the densest subgraph discovery (DSD) problem has found a wide spectrum of real applications, such as discovery of filter bubbles in social media, finding groups of actors propagating misinformation in social media, social network community detection, graph index construction, regulatory motif discovery in DNA, fake follower detection, and so on. Theoretically, DSD closely relates to other fundamental graph problems, such as network flow and bipartite matching. Triggered by these applications and connections, DSD has garnered much attention from the database, data mining, theory, and network communities. In this survey, we first highlight the importance of DSD in various real-world applications and the unique challenges that need to be addressed. Subsequently, we classify existing DSD solutions into several groups, which cover around 50 research papers published in many well-known venues (e.g., SIGMOD, PVLDB, TODS, WWW), and conduct a thorough review of these solutions in each group. Afterwards, we analyze and compare the models and solutions in these works. Finally, we point out a list of promising future research directions. It is our hope that this survey not only helps researchers have a better understanding of existing densest subgraph models and solutions, but also provides insights and identifies directions for future study.

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 manuscript is a survey on densest subgraph discovery (DSD) that first motivates the problem via applications in social media analysis, misinformation detection, community detection, and bioinformatics, then classifies roughly 50 papers from venues including SIGMOD, PVLDB, TODS, and WWW into several groups, reviews the solutions in each group, compares the models, and lists future research directions.

Significance. A well-executed survey with representative coverage would organize a fragmented literature across database, data mining, theory, and network communities and help identify open problems; the manuscript's explicit mention of cross-community attention and concrete applications is a strength, but the absence of a documented selection protocol limits its immediate utility as a reference.

major comments (2)
  1. [Abstract] Abstract: the central claim that the survey 'classify[es] existing DSD solutions into several groups, which cover around 50 research papers ... and conduct[s] a thorough review' is load-bearing, yet the text provides no description of the literature search protocol, databases queried, inclusion/exclusion criteria, or date range; without these, it is impossible to assess whether the selected set is representative or whether major omissions or misclassifications have occurred.
  2. [Abstract] Abstract / Introduction: the assertion of 'non-overlapping' groups and 'thorough review' cannot be evaluated because the manuscript does not list the groups, the assignment criteria, or any cross-check against an exhaustive bibliography of DSD papers; this directly affects the reliability of the subsequent comparison and future-directions sections.
minor comments (1)
  1. [Abstract] The abstract lists example applications but does not indicate whether each cited paper is later reviewed in the corresponding group; adding forward references would improve traceability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight opportunities to improve the transparency of our survey methodology. We agree that additional details on literature selection and classification criteria will strengthen the manuscript and will incorporate revisions to address both major points.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the survey 'classify[es] existing DSD solutions into several groups, which cover around 50 research papers ... and conduct[s] a thorough review' is load-bearing, yet the text provides no description of the literature search protocol, databases queried, inclusion/exclusion criteria, or date range; without these, it is impossible to assess whether the selected set is representative or whether major omissions or misclassifications have occurred.

    Authors: We acknowledge this limitation in the current version. The abstract and introduction do not describe the search protocol. In the revision we will add a dedicated subsection (likely in Section 1 or a new Section 2) that specifies: (i) the primary venues and databases considered (SIGMOD, PVLDB, TODS, WWW, VLDBJ, KDD, ICDE, and arXiv preprints), (ii) the approximate date range (papers up to early 2023), and (iii) inclusion criteria focused on works that propose novel DSD models, algorithms, or theoretical results with empirical evaluation. This will allow readers to judge coverage and potential gaps. revision: yes

  2. Referee: [Abstract] Abstract / Introduction: the assertion of 'non-overlapping' groups and 'thorough review' cannot be evaluated because the manuscript does not list the groups, the assignment criteria, or any cross-check against an exhaustive bibliography of DSD papers; this directly affects the reliability of the subsequent comparison and future-directions sections.

    Authors: We agree that the abstract should preview the classification scheme. The body of the manuscript organizes papers into groups (exact vs. approximate, static vs. dynamic, homogeneous vs. heterogeneous, etc.) with assignment based on the dominant technical approach. In the revision we will: (a) explicitly list the groups and their assignment criteria in the abstract/introduction, (b) add a summary table mapping each of the ~50 papers to its group, and (c) clarify that groups are intended to be non-overlapping by primary technique while noting that some papers could fit multiple categories. We will also state the scope limitations and that the list is representative rather than exhaustive. revision: yes

Circularity Check

0 steps flagged

Survey paper with no derivations or self-referential reductions

full rationale

This paper is a literature survey that classifies and reviews ~50 external papers on densest subgraph discovery. It contains no mathematical derivations, fitted parameters, predictions, or ansatzes. The central claims rest on summarizing published external work rather than any internal chain that reduces to the paper's own inputs or self-citations. No load-bearing step matches any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a survey paper; it introduces no new mathematical claims, fitted parameters, axioms, or postulated entities. All content rests on previously published work that the authors cite.

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Reference graph

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