  We study graph parameters whose associated edge-connection matrices have
exponentially bounded rank growth. Our main result is an explicit construction
of a large class of graph parameters with this property that we call mixed
partition functions. Mixed partition functions can be seen as a generalization
of partition functions of vertex models, as introduced by de la Harpe and
Jones, [P. de la Harpe, V.F.R. Jones, Graph invariants related to statistical
mechanical models: examples and problems, Journal of Combinatorial Theory,
Series B 57 (1993) 207--227] and they are related to invariant theory of
orthosymplectic supergroup. We moreover show that evaluations of the
characteristic polynomial of a simple graph are examples of mixed partition
functions, answering a question of de la Harpe and Jones.
