Is emptiness interdependence and interrelationship? Emptiness is described in a number of ways however i am interpreting it as interdependence and interrelationships. Is this an appropriate understanding?
I would say yes, it is a [seemingly] valid understanding.

Usually, from a Madhyamika-Prasangika point of view, it is stated that:


  The meaning of emptiness is dependent-arising; and the meaning of dependent-arising is emptiness.


See Tsongkhapa's Ocean of Reasoning, page 501... Geshe Lhundrup Sopa's Steps on the Path to Enlightenment, page 138, and so forth.

A simple example is as follows: the person is merely imputed in dependence upon any of its aggregates. The person is neither intrinsically one with her body (or any other aggregate), nor intrinsically different from it, but is labeled in dependence upon it. When I see John's body, I say "I see John", when I hear John's voice, I say "I hear John", when John's body is in the garden, I say "John is in the garden", and because his body is ugly, I say "John is quiet ugly". This is because John is imputed (and exists) in dependence upon that which he is not (he is not his body, he is not his voice, and so forth) but without which he would not exist. The meaning of emptiness [of inherent existence], according to Madyhamika-Prasangika, is that if you look for it with a mind analyzing the ultimate, you will not find it.


In Nagarjuna's Sixty Stanzas of Reasoning, it says:


  It is said to be by the supreme knowledge of suchness, The seeing of
  dependent-arising, that what Is dependently produced is not
  [inherently] produced.



Dependent arising is called 'the king of reasoning' because it leads to a correct understanding of emptiness and avoids the two extremes.

According  to Prasangika, they are three types of  dependent-arising. It is a tenet unique to Prasangika.


Causal dependence. Example: a seed and a sprout.
Dependence in relation to parts. Example: short and long.
Dependence on name. The meaning of which I explained in relation to John.