Generalized quasirandom graphs
Journal of Combinatorial Theory Series B
Connections between probability estimation and graph theory
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Graph homomorphisms with complex values: a dichotomy theorem
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
A Complexity Dichotomy for Partition Functions with Mixed Signs
SIAM Journal on Computing
The large deviation principle for the Erdős-Rényi random graph
European Journal of Combinatorics
Distinguishing graphs by their left and right homomorphism profiles
European Journal of Combinatorics
The rank of edge connection matrices and the dimension of algebras of invariant tensors
European Journal of Combinatorics
The complexity of the counting constraint satisfaction problem
Journal of the ACM (JACM)
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Connection matrices were introduced in [M. Freedman, L. Lovász, A. Schrijver, Reflection positivity, rank connectivity, and homomorphism of graphs (MSR Tech Report # MSR-TR-2004-41) ftp://ftp.research.microsoft.com/pub/tr/TR-2004-41.pdf], where they were used to characterize graph homomorphism functions. The goal of this note is to determine the exact rank of these matrices. The result can be rephrased in terms of the dimension of graph algebras, also introduced in the same paper. Yet another version proves that if two k-tuples of nodes behave in the same way from the point of view of graph homomorphisms, then they are equivalent under the automorphism group.