Skip to content

task_graph__node_link__largest_component_size

Program Contract

Program: count(nodes(argmax(connected_components(graph), metric=size))); scene=node_link; scope=largest_component_size

Candidate set: the visible graph, tree, network, route, matrix, table, node, edge, label, weight, path, and option elements inside the largest_component_size objective scope. Operands: visible scene state and prompt-bound operands named by nodes, argmax, connected_components, graph, metric, size, node_link, largest_component_size. Operation: evaluate count over the candidate set using the visible graph structure, labels, weights, directions, reachability, paths, connectivity, or option-selection constraints encoded in the program expression; generation enforces a unique final answer. Output binding: answer uses the integer schema; generation binds a unique final answer. Annotation witnesses: annotation uses the point_set schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: single.

Reasoning Operations

Families: counting, ranking, topology

Summary

  1. Domain: graph
  2. Scene id: node_link
  3. Scene: comparison
  4. Task id: task_graph__node_link__largest_component_size
  5. Objective: return the size of the unique largest connected component.

Query IDs

  1. single
  2. Query ids are internal replay metadata; public sampling is at the task-id level.

Answer And Annotation

  1. Answer type: integer.
  2. Annotation type: point_set.
  3. Annotation marks minimal pixel-space visual witnesses for the answer, not answer labels or non-witness annotations.
  4. Count tasks require answer_gt.value == len(annotation_gt.value) unless the annotation schema is keyed or sequence based.

Rendering Contract

  1. The scene uses the graph-domain renderer for node_link.
  2. Visual style, fonts, panel treatment, layout jitter, and post-render noise are non-semantic and must be recorded in trace metadata.
  3. Annotation projection is computed after final layout and style placement.

Prompt Contract

  1. Prompt text comes from graph prompt templates and scene config, not hardcoded user-facing text.
  2. Answer mode emits {"answer": ...}.
  3. Answer-and-annotation mode emits {"annotation": ..., "answer": ...} with annotation matching the schema above.