In the process of calculating the admittance matrix of a fairly large

-port network of

nodes, we are often confronted with the problem of seeking that order of the pivotal condensations with respect to

internal ports of the primitive admittance matrix. Motivated by this problem, we discuss a method of decomposing a given graph.into "compactly connected" two-terminal subgraphs. The decomposition enables us to apply the block-pivoted condensation on the nodal admittance matrix.