This chapter introduces a matrix, the kth connection matrix, for a given graph parameter and integer k ≥ 0. The properties of these matrices are closely connected with properties of the parameter. For example, the rank of this matrix is considered the minimum number of real numbers that has to be communicated across a node-cut of size k in order to evaluate the invariant. It is shown that other properties of this matrix, like whether it is semidefinite, also turn out to have graph theoretic significance.
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