This talk introduces the notion of normal factor graphs (NFGs) under a new semantics, namely, the "exterior function" (or "partition function") semantics. The main purpose of this talk is to discuss the ability of NFGs to model, and link, various notions from distinct fields. I will start by showing how Valiant's Holant theorem (for holographic reduction) and Forney's duality theorem (for codes on graphs) can be unified under the framework of NFGs via the notion of holographic transformations. Then, I will introduce NFGs as an algebraic tool, point out their relation to Trace Diagrams, and present few examples illustrating their possible use to (diagrammatically) establish some linear-algebraic results. Finally, I will briefly discuss NFGs as a probabilistic model, where existing graphical models such as factor graphs, convolutional factor graphs, and cumulative distribution networks may be recovered from the NFGs model.