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Christian Borgs

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Highlights from Current Programs part 2:Eighth Annual Industry Day2022-11-16
Three short programs report concrete tools and open claims: a graph limit (graphon) model that generates sparse networks from two-feature link functions and…
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Graphons and Graph Limits 1Graph Limits and Processes on Networks: From Epidemics to Misinformation Boot Camp2022-08-29
Dense graph sequences have a single concrete limit object: graphon = W:[0,1]^2→[0,1], a symmetric feature-kernel that generates inhomogeneous random graphs by…
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Graphons and Graph Limits 2Graph Limits and Processes on Networks: From Epidemics to Misinformation Boot Camp2022-08-29
Defines dense graph limits as graphons and shows that cut metric convergence is equivalent to matching subgraph frequencies, sampled-k distributions…
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Locally Convergent GraphsGraph Limits and Processes on Networks: From Epidemics to Misinformation Boot Camp2022-08-29
Sequence convergence uses the rooted-ball metric: pick a vertex uniformly, record the radius-R ball, and set distance = 1/(R+1) where balls are isomorphic…
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