Things like that have been around for a long time. It was like two decades ago that I saw this shader scheme in softimage|xsi.

For implementing something like that, each node in that graph would have an array of inputs and outputs. Each of those would have a type like vector, scalar, colour, string. Then you only allow connections if the inputs and outputs match types (though you can also have conversion nodes or selectors that say pick the red channel of a colour to turn it into a scalar). Each input can be set to a constant value instead of connecting something else to it. Outputs don't need to be connected, which is mostly useful if a node has multiple outputs. Then each node has an evaluation function that takes all input parameters and maybe internal configuration parameters (though you might as well make everything an input param since there's no real functional difference) and uses them to calculate the outputs, which it then sends on to anything connected to those.

I'm not much of a UI guy but displaying it for the GUI would just involve drawing boxes or some shape for the node, then spaces for each of the inputs on the left side and outputs on the right side maybe colour code them by type, and lines running along the connections. Then just add the name and/or other visual information you want to display and positional information to let users move it around their work area.