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We present a unified mathematical derivation of the asymptotic behaviour ofthree of the main forms of \textit{directed transfer function} (DTF)complementing recent partial directed coherence (PDC) results\cite{Baccala2013}. Based on these results and numerical examples we argue fora new directed `link' centered neural connectivity framework to replace thewidespread correlation based effective/functional network concepts so thatdirected network influences between structures become classified as to whetherlinks are \textit{active} in a \textit{direct} or in an \textit{indirect} waythereby leading to the new notions of \textit{Granger connectivity} and\textit{Granger influenciability} which are more descriptive than speaking ofGranger causality alone.

Consolidating a Link Centered Neural Connectivity Framework with Directed Transfer Function Asymptotics