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Graph conductance

As explained in Knowledge Graphs and LLMs in Action

Graph conductance is a measure of the connectivity between a subgraph and the remainder of its graph relative to the connections incident to the subgraph.

Graph conductance measures how independently a subgraph is separated from the rest of its graph. It counts edges crossing the subgraph boundary relative to edges incident to the subgraph, producing a value from 0 to 1. Lower conductance indicates a tighter-knit, more independent community. section 4.2.3

A practical conductance analysis follows this pipeline:

  • Extract the disease-associated proteins and their interaction edges into a subgraph. section 4.2.3
  • Query interactions connecting pathway proteins to proteins outside the pathway and count distinct boundary edges. section 4.2.3
  • Compare the boundary result with the pathway’s incident edges to interpret external connectedness. section 4.2.3

Disease pathways in a PPI network

Disease pathways have a median conductance of 0.96, indicating strong external connectivity despite higher internal density than the overall PPI network. Conductance distributions help compare pathway organization across diseases. section 4.2.3

Figure 4.7 Distributions of the three key measures for disease pathways
figure

Inspect the conductance distribution alongside pathway density and largest-component size. section 4.2.3

How Knowledge Graphs and LLMs in Action covers it

How deep it goes
Defines the normalized metric and implements boundary-edge counting, but does not provide its complete denominator calculation.
Examples
Uses disease pathways, protein–protein interaction networks, boundary-edge Cypher queries, and conductance distributions.
What you can do after
Diagnose with it whether extracted pathways are internally cohesive or externally entangled with the broader network.
How it connects
Connects conductance with graph density, connected components, Louvain clustering, and knowledge-graph quality analysis.

Related concepts

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.