How many edges are cut in a balanced partition of a graph? Consider a graph on n nodes and e edges that is partitioned into k "balanced" subgraphs in the sense that each block has an equal number of nodes and the number of cut edges is minimized. Is there a formula for the number of cut edges in this situation?
Even in the current updated version of the question, it still remains ill defined. There many different ways by which you can partition a graph into symmetric (or balanced if you like) clusters. One question that you might have in mind but have problem expressing is the minimum multisection (or partition): Given a graph $G$ find a symmetric partition $P$ of its vertices such that it minimizes the edges between different clusters.

In which case the answer is that the problem is NP-hard [1] and moreover it is NP-hard to approximate within a constant factor [2].

[1] L. Hyafil and R. L. Rivest. Graph partitioning and constructing optimal decision trees are polynomial complete problems. 1973.

[2] K. Andreev and H. Racke. Balanced graph partitioning. 2004.