Efficient Calculation of Triangle Centrality in Big Data Networks
Bibliographic record
Abstract
The notion of “centrality” within graph analytics has led to the creation of well-known metrics such as Google's Page Rank [1], which is an extension of eigenvector centrality [2]. Triangle centrality is a related metric [3] that utilizes the presence of triangles, which play an important role in network analysis, to quantitatively determine the relative “importance” of a node in a network. Efficiently counting and enumerating these triangles are a major backbone to understanding network characteristics, and linear algebraic methods have utilized the correspondence between sparse adjacency matrices and graphs to perform such calculations, with sparse matrix-matrix multiplication as the main computational kernel. In this paper, we use an intersection representation of graph data implemented as a sparse matrix, and engineer an algorithm to compute the triangle centrality of each vertex within a graph. The main computational task of calculating these sparse matrix-vector products is carefully crafted by employing compressed vectors as accumulators. As with other state-of-the-art algorithms [4], our method avoids redundant work by counting and enumerating each triangle exactly once. We present results from extensive computational experiments on large-scale real-world and synthetic graph in-stances that demonstrate good scalability of our method. We also present a shared memory parallel implementation of our algorithm.
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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 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".