Due to the separation of any total graph into two partial graphs of equivalent structure one obtains one additional degree of freedom (df) per any further edge added, regarding its position within the partial graph. Thus, as every numbering starts with vertex 1, the number of df's will be reduced by one as compared to the number of edges. If we intend to add symmetry, regarding the order of vertices, we will gain one additional df per edge, apart from the first one. All these dfs gained by the separation process make it possible to reduce the number of all total graphs to a comparable minimum of partial graphs.

The price of separation is the necessity to join two partial graphs to obtain a total graph later on. However, this expense appears to be small as compared to the profit rising from less extended calculations of the partial graphs.

Two further peculiarities support the calculations of the minimum number of partial graphs:
1.
For once the frequency distribution of the numerical values of all partial graphs (as well as of the total graphs) is similar to the shape of a normal distribution, so that its lower tail will contain comparably few partial graphs.
2. 
On the other hand one can make use of the trivial fact that, given two terms of numeric values, the smaller one will reach half of the total sum at most. Starting from the smallest total graph, gained from the current calculation, one has only got to regard the set of partial graphs with the numerical values running up to no more than half of that of the smallest calculated graph. 

Furthermore one can reduce the time of calculation by way of skillful numbering of the vertices and, quite traditionally, by way of lowering the numerical values of edges by a constant amount.

However, the true peculiarity of the ZIP-method may be seen in reducing the number of total graphs to a minimum number of partial graphs. Hence, the ZIP-method is not bound to replace other and different solutions, but it may be combined with them or even be preadapted.


(24.05.2003: translated by Prof. Dr. Klaus Höher, München)