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Radicchi edge-clustering community detection

Algorithms AIMech:RadicchiEdgeClustering DRAFT

Aliases: Radicchi divisive algorithm, modified edge-clustering community detection

A divisive graph-community algorithm family that repeatedly removes edges with the lowest modified cycle-based edge-clustering score, updates affected local scores and forms a component hierarchy, optionally retaining branches through the paper’s original-adjacency strong or weak community tests.

Identity Notes & Concept Scope Compared all 442 pinned AIO and 675 native IDs, names, aliases and scoped synonyms before either cohort write; no normalized identity match. Ignored- and hidden-inclusive searches of all three checkouts returned 16,0,0 lines. All sixteen public matches were read: source citations, previously pending reading notes, query logs and the existing Radicchi source lead, not either maintained identity. Semantic assessment covered 64 AIO and 290 native definitions: 46 AIO and 268 native rows match prior inspected context; all 18 newly selected AIO and 22 native definitions were read. Sixteen complete AIO node/edge/generated contexts were verified unchanged and mapping rationales reassessed. Both drafts were compared for inherited betweenness plus definition filtering versus local cycle-score deletion. Retain the modified edge-clustering divisive family, with the explicit triangle rule and described higher-cycle extension. Its minimum local cycle score differs from maximal shortest-path betweenness even though either selector can use the same definition filter. This family record does not create an extra g3 duplicate or assert an inspected complete g4 implementation.

Claims & Grounded Evidence

7 Claims

Mechanism #modified-triangle-score

For an edge joining vertices i and j, the triangle variant scores (z + 1) / min(k_i − 1, k_j − 1), where z counts triangles containing the edge and k values are current endpoint degrees. It removes edges with smallest scores and updates affected values. The added one distinguishes this ranking from the ordinary edge-clustering coefficient; values may exceed one, as exact scores of two on a triangle and three-halves on a four-clique illustrate.

supports Source: Defining and identifying communities in networks · Locator: Section IV, PDF pp. 4–5, Equations 3–4 and update discussion; curator calculation in research/discovery/radicchi-boundaries.py

Limitation #leaf-and-tie-boundary

The source assigns an infinite modified score to a leaf’s unique edge, whose triangle denominator is zero. This is a stated convention, not a finite probability. A triangle-free four-cycle instead gives equal finite triangle scores of one. The inspected text does not settle every tie or terminal all-infinite case, so the record does not claim that a leaf edge can never be removed during full-tree construction.

supports Source: Defining and identifying communities in networks · Locator: Section IV, PDF p. 5, paragraph following Equation 5; Figure 5 legend, pp. 8–9; curator calculation in research/discovery/radicchi-boundaries.py

Scope #cycle-family-boundary

The family extends the score to (z_g + 1) / s_g using the number of cycles of order g containing an edge and the possible such cycles given the node degrees. The paper evaluates triangles and four-cycles, but the inspected presentation gives no explicit executable four-cycle denominator formula. This record preserves the described family without claiming reconstruction of a particular g = 4 implementation.

supports Source: Defining and identifying communities in networks · Locator: Section IV, PDF p. 5, Equation 5 and g = 3/g = 4 discussion

Mechanism #selector-and-filter

Minimum modified cycle score replaces maximum shortest-path betweenness as the edge selector. The plotted anticorrelation between those scores is imperfect and their extremal edges can differ. Either selector can be combined with the same original-adjacency community tests and at-least-two-qualifying-children retention rule; sharing a filter does not establish identical hierarchies.

supports Source: Defining and identifying communities in networks · Locator: Sections III–IV, PDF pp. 4–5; Figure 4 legend p. 8 and plot p. 12

Limitation #runtime-conditions

The paper’s rough aM + bM-squared cost estimate combines repeated connectivity checks with local score updates. Treating an update as independent of total edge count requires control of the local neighborhood and cycle order; it is not a universal constant-cost claim for unbounded degrees. Figure 5 measures full-tree construction without a community-validation criterion on random graphs of fixed average degree five, so its times are not complete filtered-pipeline timings.

supports Source: Defining and identifying communities in networks · Locator: Section IV, PDF p. 5, runtime estimate; Figure 5 legend, pp. 8–9 and plot p. 13

Scope #evaluation-scope

On the 128-vertex four-group synthetic benchmark with expected degree sixteen, the paper compares strong/weak definition outcomes and exact-group success separately from node error. Its g = 4 weak-criterion advantage is conditional on that test. The collaboration case analyzes the largest 12,722-vertex component of a 15,616-vertex graph; its reported size distribution pools nested weak communities, not merely groups from one flat partition.

supports Source: Defining and identifying communities in networks · Locator: Sections III–V, PDF pp. 4–6; Figure 2 and Figure 6 legends, pp. 8–9, plots pp. 10 and 14

Limitation #domain-limits

The source’s applications are social networks. It acknowledges subjective interpretation of collaboration groups and identifies a shortage of short cycles as a possible difficulty for non-social networks. Proposed biological and technological applications are future work in this source, not demonstrated general validation or proof that few triangles mean no communities exist.

supports Source: Defining and identifying communities in networks · Locator: Sections V–VI, PDF pp. 6–7

⚠️ Curated Limitations & Negative Results

This family record covers arXiv cond-mat/0309488v2, with an explicit triangle formula and bounded description of higher-cycle scoring. It is not a duplicate standalone g3 record or a complete implementation specification for g4.
Current-graph degrees and cycles determine deletion scores; the optional strong/weak community tests use the original full adjacency. Conflating these two graph states changes the procedure.
The finite calculations test score and definition boundaries only. They do not run author code or reproduce the source’s accuracy and runtime experiments.
Source tie resolution, higher-cycle denominator conventions and terminal all-infinite behavior were not audited in code. Weighted and directed generalizations are outside the inspected scope.
All fourteen text pages, equations and figures were inspected. The journal PDF, supporting community lists, datasets and author software remain uninspected. No model training or benchmark replication was performed; the record remains DRAFT.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:HierarchicalClustering` Hierarchical Clustering	related_match	Successive graph splits produce a grouping hierarchy; the AIO task is related to this particular divisive family rather than equivalent to it.
`AIO:UnsupervisedClustering` Unsupervised Clustering	related_match	Local graph scores and optional degree tests produce unlabeled groupings from topology without class-label supervision.

Evidence Sources & Primary Literature

1 Source

Source ID	Publication / Document	Type / Access	Reference & Checksum
`radicchi2004`	Defining and identifying communities in networks Filippo Radicchi, Claudio Castellano, Federico Cecconi, Vittorio Loreto, Domenico Parisi	primary paper full_text	ID: arxiv:cond-mat/0309488v2 sha256:02467f9e119b…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-14T02:08:28Z

Updated: 2026-10-14T02:08:28Z

Source File: data/curated/RadicchiEdgeClustering.yaml