Numerous studies indicate that the genome of higher eukaryotes is organized into distinct chromosome territories and that the 3-D arrangement of these territories may be closely connected to genomic function and the global regulation of gene expression. Despite this progress, the degree of non-random arrangement remains unclear and no overall model has been proposed for chromosome territory associations. To address this issue, a re-FISH approach was combined with computational analysis to analysis the pair-wise associations for six pairs of human chromosomes (chr #1, 4, 11, 12, 16, 18) in the G(0) state of normal human WI38 lung fibroblast and MCF10A epithelial breast cells. Similar levels of associations were found in WI38 and MCF10A for several of the chromosomes whereas others showed striking differences. A novel computational geometric approach, the generalized median graph (GMG), revealed a preferred probabilistic arrangement distinct for each cell line. Statistical analysis demonstrated that approximately 50% of the associations depicted in the GMG models are present in each individual nucleus. A nearly twofold increase of chromosome 4/16 associations in a malignant breast cancer cell line (MCFCA1a) compared to the related normal epithelial cell line (MCF10A) further demonstrates cancer related changes in chromosome arrangements. Our findings of highly preferred chromosome association profiles that are cell type specific and undergo alterations in cancer cells, lead us to propose a probabilistic chromosome code whereby the 3-D association profile of chromosomes contributes to the functional landscape of the cell nucleus, the global regulation of gene expression and the epigenetic state of chromatin.