Path-degree product

As explained in Knowledge Graphs and LLMs in Action

Path-degree product is the product of degree values raised to a damping exponent for all edge incidences along a path.

The path-degree product (PDP) assigns a connectivity-adjusted value to an individual knowledge-graph path. Extract the two metaedge-specific degree values for every edge incidence, raise each degree to −w, where w ≥ 0 is the damping exponent, and multiply the results. section 4.3

A practical PDP calculation follows this pipeline:

• Select a path matching the required metapath. section 4.3
• Record both relationship-specific degree values contributed by each edge. section 4.3
• Apply the damping exponent to every degree and multiply the resulting values; summing PDPs across paths produces the DWPC for that metapath. section 4.3

IRF1 to multiple sclerosis

For the path IRF1—INTERACTS—CXCR4—[relationship]—multiple sclerosis, the IRF1–CXCR4 edge contributes degree values 4 and 2. With w = 0.5, exponentiate each degree by −0.5 and multiply it with the corresponding factors from the remaining edge incidences. section 4.3

Figure 4.10 (a) Extracting paths based on a defined metapath, and (b) computing the path-degree product (PDP) and DWPC

Use the figure to follow metapath-based path extraction and the corresponding PDP and DWPC computations. section 4.3

How Knowledge Graphs and LLMs in Action covers it

How deep it goes

Explains degree extraction, exponentiation, multiplication, and aggregation into DWPC, without deriving the full formula.

Examples

Uses IRF1, CXCR4, multiple sclerosis, and degree pairs such as 4 and 2 in a worked path calculation.

What it assumes

Assumes knowledge-graph paths and metapaths while defining metaedge-specific degrees and the damping exponent.

What you can do after

Evaluate knowledge-graph paths and aggregate their PDP values into a metapath-level DWPC.

How it connects

Connects path-degree product with metapaths, metaedges, degree values, DWPC, and knowledge-graph path prevalence.

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Related concepts

• degree-weighted path countpart of · A degree-weighted path count is a path-based graph metric that weights paths according to the degrees of the entities they traverse.
• damping exponentconfigured by · A damping exponent is a nonnegative exponent that controls how graph degree values reduce the contribution of a path.

This explainer was generated by Manning's knowledge graph from the text of Knowledge Graphs and LLMs in Action. The section links point to the parts of the book it draws on.