Asymptotic Enumeration of Spanning Trees
Combinatorics, Probability and Computing
Graph invariants in the spin model
Journal of Combinatorial Theory Series B
Note: Dual graph homomorphism functions
Journal of Combinatorial Theory Series A
Continuum limits for classical sequential growth models
Random Structures & Algorithms
Connections between probability estimation and graph theory
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Parameter testing in bounded degree graphs of subexponential growth
Random Structures & Algorithms
Property testing and parameter testing for permutations
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Testing permutation properties through subpermutations
Theoretical Computer Science
Journal of Combinatorial Theory Series B
The minimum size of 3-graphs without a 4-set spanning no or exactly three edges
European Journal of Combinatorics
The large deviation principle for the Erdős-Rényi random graph
European Journal of Combinatorics
Limits of randomly grown graph sequences
European Journal of Combinatorics
Limits of kernel operators and the spectral regularity lemma
European Journal of Combinatorics
Quasi-random graphs and graph limits
European Journal of Combinatorics
Testability of minimum balanced multiway cut densities
Discrete Applied Mathematics
Journal of Graph Theory
SIAM Journal on Discrete Mathematics
A note on permutation regularity
Discrete Applied Mathematics
Limits of permutation sequences
Journal of Combinatorial Theory Series B
Estimation of exponential random graph models for large social networks via graph limits
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
On the number of B-flows of a graph
European Journal of Combinatorics
Computers & Mathematics with Applications
Limits of local algorithms over sparse random graphs
Proceedings of the 5th conference on Innovations in theoretical computer science
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We show that if a sequence of dense graphs G"n has the property that for every fixed graph F, the density of copies of F in G"n tends to a limit, then there is a natural ''limit object,'' namely a symmetric measurable function W:[0,1]^2-[0,1]. This limit object determines all the limits of subgraph densities. Conversely, every such function arises as a limit object. We also characterize graph parameters that are obtained as limits of subgraph densities by the ''reflection positivity'' property. Along the way we introduce a rather general model of random graphs, which seems to be interesting on its own right.