---
title: "algorithm-k-core — Mova code model"
description: "Mova code model of algorithms/src/k_core/mod.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/k_core/mod.rs.groupant/"
---
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# algorithm-k-core

The groupant beside algorithms/src/k_core/mod.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

## Facts

- **kind:** groupant
- **status:** partial source derived instance
- **source:** [`algorithms/src/k_core/mod.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/k_core/mod.rs)
- **source SHA-256:** `37a416e1386fa1f7…`
- **repository folder:** [`algorithms/src/k_core/mod.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/k_core/mod.rs.groupant)
- **repository commit:** `855da7bd4a7b`

> **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.

## Components

| component | label | where |
|---|---|---|
| **approximant** | bounded checked | [Forward](#forward) |
| **ast** | partial | `syntax.json` |
| **cost** | symbolic unmeasured | [Cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | source derived | [Invariant](#invariant) |
| **tests** | bounded executed | [evidence](#evidence) |

## Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

| id | type | label | where |
|---|---|---|---|
| `nonbehavior` | behavior_complement | partial source derived | [nonbehavior](#nonbehavior) |
| `compatible_inputs` | reverse_reconstruction | partial source derived | [compatible_inputs](#compatible-inputs) |
| `subset_certificate` | maximality_certificate | partial source derived | [subset_certificate](#subset-certificate) |
| `nested_cores` | parameter_monotonicity | partial source derived | [nested_cores](#nested-cores) |
| `idempotence` | fixed_point | partial source derived | [idempotence](#idempotence) |
| `edge_extension` | monotone_extension | partial source derived | [edge_extension](#edge-extension) |

## Model text


Migration: consolidated into model.md, 2026-11-04, operator decision; fresh hash-bound references to the former files were rebound to the sections below.

### descriptant

#### k_core mod

Original std-only Rust. Prospective model is retained beside implementation. Source citations identify algorithm provenance; no copied implementation. Exact bounded graph semantics are useful independently of any unmeasured optimization. Finite oracle checks and mutant discrimination improve confidence; groupant count alone proves no improvement.

### model

## k_core mod model

### Forward

Simple undirected graph n<=256,m<=65536. Repeatedly delete vertices with live degree below k; return ascending survivors, unique maximal induced minimum-degree-k subgraph. FIFO deletion, each edge visited O(1) after O(V^2+E) validation. O(V^2+E) time/storage. k=0 retains all. Seidman (1983).

### Invariant

Deleted vertices cannot belong to any minimum-degree-k induced subgraph. For live vertices degree equals count of live neighbors; survivor set is maximal.

### Cost

Simple undirected graph n<=256,m<=65536. Repeatedly delete vertices with live degree below k; return ascending survivors, unique maximal induced minimum-degree-k subgraph. FIFO deletion, each edge visited O(1) after O(V^2+E) validation. O(V^2+E) time/storage. k=0 retains all. Seidman (1983).

### nonbehavior

Type: behavior_complement. Let R be the deterministic relation specified by Forward including validation precedence and tie rules, X the declared input type and Y its Result type. Behavior complement is (X times Y) minus R. Specifically outputs violating Deleted vertices cannot belong to any minimum-degree-k induced subgraph. For live vertices degree equals count of live neighbors; survivor set is maximal. are excluded; a valid-input Err or a wrong successful witness is excluded. Resource, cycle and structural rejections are determined before algorithmic output.

### compatible_inputs

Type: reverse_reconstruction. Given survivor set S, compatible graphs make G[S] minimum degree at least k and every vertex outside S eventually peelable. For k=1, a three-vertex path and a triangle differ but both can yield all vertices when no isolated vertices. Errors identify violated validation predicates.

### subset_certificate

Type: maximality_certificate. Output equals union of all vertex subsets whose induced minimum degree is at least k. Union preserves the minimum-degree predicate and gives unique maximality.

### nested_cores

Type: parameter_monotonicity. For k<=l, core_l(G) is a subset of core_k(G). core_0(G) is every vertex; k>=n gives empty on simple n-vertex graphs.

### idempotence

Type: fixed_point. Restrict G to returned vertices, retaining their labels. Applying k-peeling again deletes none.

### edge_extension

Type: monotone_extension. Adding an absent undirected edge cannot remove vertices from a k-core; the prior induced feasible set still witnesses membership.

### Limits

Partial syntax omits macro expansion and type resolution. No executable approximate profile: categorical graph semantics and feasibility have no justified percentage relaxation here. Integer operations are bounded by caps; flow uses checked i128/u64 arithmetic, with Overflow defensive under current caps. No callbacks. Allocator failure is outside typed status.

### evidence

#### Evidence — 2026-10-30

Eleven tests across five algorithms, including independent exhaustive small-domain characterization. This file belongs to k_core. Two debug and two optimized runs matched normalized statuses. Strict clippy-driver --test -D warnings passed. A compiled production mutant failed a named assertion; exact bytes restored and positive rerun passed. Raw receipts: $MOVA_DATA/runs/octopus-wave25-graphs-2026-10-30/k_core-*.txt. No timing or whole-system improvement claim. Source SHA-256: 37a416e1386fa1f72fcf9fa8771e88af0a2a98d0bf51b94df3605c8462065707.

### prospective

#### Prospective model — 2026-10-30

Simple undirected graph n<=256,m<=65536. Repeatedly delete vertices with live degree below k; return ascending survivors, unique maximal induced minimum-degree-k subgraph. FIFO deletion, each edge visited O(1) after O(V^2+E) validation. O(V^2+E) time/storage. k=0 retains all. Seidman (1983).
Allocation failure is outside typed errors. Resource caps precede vertex/edge validation. No callbacks. Exact categorical output has no justified percentage surrogate; executable approximation profiles unsupported.