Metrics

Every metric is a pure function. Some take a Formulation directly (presence flags); others take a derived Graph (structural metrics). All return a MetricResult(name, value, explanation, data).

Presence flags

Name	Source	Definition	Differentiating example
has_big_m	model	A parameter has kind="big_m" or a constraint has kind="big_m".	mip_2_1_big_m is True; mip_2_4_time_indexed is False.
has_integer_vars	model	Any variable template has domain integer or binary.	True for every MIP/MILP; False for every LP.
has_modulo_offset	model	Any term binding declares modulo.	Triggers on PESP-style formulations with explicit modulo bindings.
has_soft_slack	model	Any variable has role slack or any term has role slack.	True for lp_1_5_soft_regularity.
has_aggregation_operator	model	Any term has operator != "none".	True for mip_2_4_time_indexed (sum) and objective_abs_deviation (abs).

Complexity: O(|terms|). All five computed in one pass via lp2graph.metrics.flags.presence_flags(f).

Structural metrics

Name	Source	Definition	Complexity
node_counts_by_class	graph	Count of nodes grouped by class (variable, constraint, …).	O(|V|)
edge_density	graph	\|E\| / (\|V\| · (\|V\| − 1)) for the directed graph.	O(|V| + |E|)
constraint_variable_ratio	graph	Constraint-class node count divided by variable-class node count.	O(|V|)
minimal_size	graph	\|constraints\| · \|variables\| (a weak proxy for problem size).	O(|V|)
model_coherence	graph	1 if the underlying undirected graph is connected, else 0.	O(|V| + |E|)
graph_diameter	graph	Longest shortest path in the largest connected component. Returns the path in data["path"].	O(|V| · (|V| + |E|))

All six computed in one pass via lp2graph.metrics.structural.structural_summary(g).

Constraint classification (heuristic)

lp2graph.metrics.classify_constraints(f) runs the source-repo's keyword tables (preserved verbatim) over each constraint's name and description, returning a per-constraint list of inferred type tags plus a global histogram. Use this to audit catalog tags or to cross-check author-supplied kind fields.

Determinism

Metrics are deterministic. Two calls with the same input produce identical output, byte-for-byte where applicable. Snapshot tests in tests/golden/ (planned for v0.2) will guard regressions; the existing tests verify this property by calling each metric twice and comparing.