Truss Decomposition of Probabilistic Graphs
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Bibliographic record
Abstract
A key operation in network analysis is the discovery of cohesive subgraphs. The notion of $k$-truss has gained considerable popularity in this regard, based on its rich structure and efficient computability. However, many complex networks such as social, biological and communication networks feature uncertainty, best modeled using probabilities. Unfortunately the problem of discovering k-trusses in probabilistic graphs has received little attention to date. In this paper, given a probabilistic graph G, number k and parameter γ --(0,1], we define a (k,γ)-truss as a maximal connected subgraph H ⊆ G, in which for each edge, the probability that it is contained in at least (k-2) triangles is at least γ. We develop an efficient dynamic programming algorithm for decomposing a probabilistic graph into such maximal (k,γ)-trusses. The above definition of a (k,γ)-truss is local in that the "witness" graphs that has the (k-2) triangles containing an edge in H may be quite different for distinct edges. Hence, we also propose: a global (k,γ)-truss, which in addition to being a local (k,γ)-truss, has to satisfy the condition that the probability that H contains a k-truss is at least γ. We show that unlike local (k,γ)-trusses, the global (k,γ)-truss decomposition on a probabilistic graph is intractable. We propose a novel sampling technique which enables approximate discovery of global (k,γ)-trusses with high probability. Our extensive experiments on real datasets demonstrate the efficacy of our proposed approach and the usefulness of local and global (k,γ)-truss.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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 it