[Richard777 (OP)]

Can vectors be connected to form a vector structure?
Does this structure represent a tensor?
This tensor would have two (or more) magnitudes.
Two vectors may be assumed to be “connected” if;
   - they share a common origin (tail)
   - they share a common component.
Is this a useful representation of a tensor?

[yor_on]

Richard, where do you get out from?
A global representation or a local?

[jeffreyH]

The path to your PDF is so convoluted that, by the time I got to it, I just couldn't even be bothered to read it.

[Colin2B]

Can vectors be connected to form a vector structure?

Without seeing an example it is difficult to understand what you mean.
However, by your definition of connected:

Two vectors may be assumed to be “connected” if;
   - they share a common origin (tail)
   - they share a common component.

If two vectors are arranged in this way, assuming that both magnitudes have the same denomination, then you will have a resultant vector.

Does this structure represent a tensor?

As all vectors are tensors, then if the resultant is a vector then yes.

This tensor would have two (or more) magnitudes.

Then it’s not a tensor - unless you mean components of the tensor. Give an example - don’t just link to an external website, that is not discussing a topic on this website (see our usage policy).

Is this a useful representation of a tensor?

Doesn’t sound like it.