I want to define the set of two tuples. Actually, I want to describe the degree distribution (or histogram) in terms of ordered tuples. The first item denotes the degree of a node. The second item denotes the number of items of such degree. I am using the following now:
${\cal D}=\left\{\langle d_i, \eta_i \rangle : 1 \leq i \leq \Delta \right\}$
There are $\Delta$ unique degrees. $d_i$ denotes the $i$-th unique degree. There are $\eta_i$ items with degree $d_i$.
I am struggling to define the set $\cal D$ properly with the index.
I also need to say something like the $\tau_i=\langle d_i, \eta_i \rangle$ denotes the $i$-th tuple.
Please suggest me what would be the proper mathematical vocabulary.