Network Metrics

The PCN should be summarized using a small prespecified set of interpretable metrics. The goal is not to maximize the number of graph-theoretical indices, but to capture properties that may plausibly add information beyond questionnaire severity.

Candidate global metrics

Density

Proportion of possible directed edges that are present.

Interpretation: How interconnected does the participant perceive their problems to be?

Mean causal strength

Average strength of endorsed causal relations.

Interpretation: How strongly does the participant perceive their problems to influence one another overall?

Total network strength

Sum of all edge weights.

This may be highly correlated with density and mean strength and should therefore not automatically be included together with both.

Reciprocity

Proportion of relations that are bidirectional.

Interpretation: How often are problems perceived as mutually reinforcing?

Feedback-loop indicators

Presence or number of simple directed cycles.

Interpretation: Whether the participant perceives self-reinforcing causal chains.

Candidate node-level summaries

Maximum out-strength

Strength of the most influential perceived driver.

Out-strength dispersion

Degree to which outgoing influence is concentrated in a small number of nodes.

This may distinguish:

• distributed systems, in which many problems influence one another similarly,
• from driver-dominated systems, in which one or two problems account for much of the outgoing influence.

Maximum in-strength

Degree to which one problem is perceived as especially downstream of others.

Prespecification principle

For confirmatory analyses, use a compact block such as:

• density,
• mean causal strength,
• out-strength dispersion.

Then compare the incremental contribution of this PCN block with the conventional questionnaire model in Validation Framework.

Important caution

Metrics should be adjusted for or interpreted in light of the number of selected nodes. Where possible, use normalized versions or include node count explicitly in the model.