Graph Clustering using Effective Resistance
Bibliographic record
Abstract
We design a polynomial time algorithm that for any weighted undirected graph G = (V, E, w) and sufficiently large \\delta > 1, partitions V into subsets V(1),..., V(h) for some h>= 1, such that at most \\delta^{-1} fraction of the weights are between clusters, i.e. \n \nsum(i < j) |E(V(i), V(j)| < w(E)/\\delta \n \nand the effective resistance diameter of each of the induced subgraphs \nG[V(i)] is at most \\delta^3 times the inverse of the average weighted degree, i.e. \n \nmax{ Reff(u, v) : u, v \\in V(i)} < \\delta^3 · |V|/w(E) \n \nfor all i = 1,..., h. In particular, it is possible to remove one \npercent of weight of edges of any given graph such that each of the \nresulting connected components has effective resistance diameter at \nmost the inverse of the average weighted degree. Our proof is based \non a new connection between effective resistance and low conductance \nsets. We show that if the effective resistance between two vertices u and v is large, then there must be a low conductance cut separating u from v. This implies that very mildly expanding graphs have constant effective resistance diameter. We believe that this connection could be of independent interest in algorithm design.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.004 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".