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Zhou first-passage attractor community detection

Algorithms AIMech:ZhouAttractorCommunityDetection DRAFT

Aliases: Zhou local and global attractor communities

A graph community-detection algorithm that forms local or global groups as the minimal nonempty sets closed under a first-passage-time attractor relation and its reverse, using neighbor-restricted or all-vertex minimum expected arrival times respectively.

Identity Notes & Concept Scope Compared both cohort candidates against all 442 pinned AIO and 697 native identities; no normalized match. Ignored- and hidden-inclusive searches of three full checkouts returned 27,0,0 lines, all read as existing Zhou source URLs, abstract interpretations, query strings and pending leads. Semantic assessment covered 155 AIO and 542 native definitions: 155 AIO and541 prior native rows verified unchanged, plus the new Noh–Rieger row and full record read. Thirteen complete AIO contexts and six full native neighbors assessed. This algorithm groups vertices by closure under minimum first-passage attractors and reverse relations. It neither deletes high-betweenness edges nor optimizes modularity, ranks individual nodes, compares complete profile vectors, or constructs a guaranteed local-to-global hierarchy.

Claims & Grounded Evidence

6 Claims

Mechanism #weighted-walk-and-distance

The maintained domain is a finite connected undirected graph with at least two vertices, symmetric nonnegative adjacency weights, positive vertex strengths and optional self-loops. The walker uses P_ij=A_ij/sum_l A_il. For target j, form B^(j) by setting column j of P to zero and solve (I-B^(j))d_:j=1. For i!=j this is the mean first-hitting time; d_jj is the positive mean return time, equal to total vertex strength divided by j’s strength. These first-passage quantities remain finite on connected periodic graphs; no convergence of the ordinary state-probability sequence is required.

supports Source: Network Landscape from a Brownian Particle’s Perspective · Locator: Graph and walk specification, PDF p. 1; Equation 1 and its linear system, p. 2; curator independent absorbing-target checks in research/discovery/zhou-walk-boundaries.py

Mechanism #all-attractor-closure

A local attractor of i minimizes d_ij over vertices adjacent to i, while a global attractor minimizes it over every vertex, including i itself. All equal minimizers satisfy the source’s non-strict inequalities. For the selected mode, a community contains every attractor of each member and every vertex attracted to a member, and is minimal among nonempty sets with both closure properties. Equivalently, the communities are weakly connected components of the directed all-attractor relation. This gives a disjoint partition without deleting original graph edges or specifying a desired number of groups.

supports Source: Network Landscape from a Brownian Particle’s Perspective · Locator: Local/global attractor definitions and three L-community conditions, PDF p. 2; weak-component equivalence is a curator interpretation of the two closure conditions

Limitation #return-and-tie-boundaries

Positive returns and ties affect the output. On a curator three-vertex path, the distance rows are (4,1,4), (3,2,3), (4,1,4); every vertex has the middle vertex as its global attractor, giving one community. Replacing diagonal returns by zero instead makes each vertex a self-attractor and yields three singleton global groups. On a four-cycle every node has two tied local attractors, giving one all-attractor component; selecting only one tied neighbor per node can instead produce two pairs. Such arbitrary tie removal is not the all-attractor rule.

supports Source: Network Landscape from a Brownian Particle’s Perspective · Locator: Equation 1 and non-strict attractor inequalities, PDF p. 2; exact path/cycle constructions in research/discovery/zhou-walk-boundaries.py

Limitation #local-global-partition-boundary

Local and global modes do not guarantee nested partitions. In a curator weighted graph with edges 0–3 of weight 2, 1–2 of weight 2, and 1–3 and 2–3 of weight 1, the local mode yields one four-node group while the global mode yields {0,3} and {1,2}. The paper’s expectation of local groups lying within global groups is heuristic. Exact curator comparison of the killed-column and independent absorbing-target equations covers all 624 connected four-vertex graphs with absent, weight-1 or weight-2 edges, totaling 2496 target systems; it is not a benchmark replication or universal recovery proof.

supports Source: Network Landscape from a Brownian Particle’s Perspective · Locator: Local/global relationship discussion, PDF p. 2; yeast relationship qualification, p. 3; finite enumeration and explicit nesting counterexample in research/discovery/zhou-walk-boundaries.py

Scope #stability-and-center-diagnostics

The instability diagnostic counts nodes whose total direct weight to some other community exceeds their weight to other members of their own community, excluding self. This compares each other community separately, rather than all outside vertices together. Stability is reported after attractor grouping and is not imposed as a membership constraint. A candidate center is a global self-attractor under the positive-return convention; existence or uniqueness is not guaranteed by the definition.

supports Source: Network Landscape from a Brownian Particle’s Perspective · Locator: Community size, instability and center definitions, PDF p. 2; unstable members reported in examples, pp. 2–3

Limitation #evaluation-and-extension-limits

The source applies the method to weighted karate and collaboration networks, an unweighted football network and a historical yeast protein-interaction component. Its planted random-module comparison reports limitations relative to Girvan–Newman, so no universal detection advantage follows. Protein transport, essentiality and functional explanations remain hypotheses rather than causal evidence. Finite-temperature membership, coarse-grained recursion, localized distance approximation and the later distance-profile dissimilarity method are separate extensions, not steps of this original attractor-closure algorithm.

supports Source: Network Landscape from a Brownian Particle’s Perspective · Locator: Examples and limitations, PDF pp. 2–3; Table I, p. 4; Figure 1, p. 5; proposed extensions, p. 3

⚠️ Curated Limitations & Negative Results

Local and global partitions are alternative output modes of one attractor-closure construction; neither is generally a refinement of the other.
The source calls expected passage a distance, but it is asymmetric and has positive diagonal returns. Replacing it by a zero-diagonal metric changes global attractors.
Exact ties are retained. Numerical tolerance and approximate linear-solver error require an implementation policy that was not audited.
The introductory stationary-probability convergence wording is not adopted for periodic walks. First-passage solves do not rely on that limit.
Only historical source applications and finite curator calculations were assessed. Journal-byte equivalence, author code, raw datasets, biological hypotheses and benchmark replication were not verified. DRAFT remains.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:UnsupervisedClustering` Unsupervised Clustering	related_match	The algorithm groups graph vertices using interaction topology and first-passage dynamics without label supervision. The AIO target denotes a clustering task, so this method-to-task relation is not an equivalence or algorithm is-a assertion.
`AIO:MarkovChain` Markov Chain	related_match	First-passage attractors are derived from a specified Markov walk. The local grouping algorithm is distinct from the target process/model; the target’s Network parent and hidden-layer relation are not imported into this graph algorithm.

Evidence Sources & Primary Literature

1 Source

Source ID	Publication / Document	Type / Access	Reference & Checksum
`zhou2003attractors`	Network Landscape from a Brownian Particle’s Perspective Haijun Zhou	primary paper full_text	ID: arxiv:physics/0302030v1 sha256:2da11ce6cf7e…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-14T08:00:11Z

Updated: 2026-10-14T08:00:11Z

Source File: data/curated/ZhouAttractorCommunityDetection.yaml