New Hi-C technologies have revealed that chromosomes have a complex network of spatial contacts in the cell nucleus of higher organisms, whose organisation is only partially understood. Here, we investigate the structure of such a network in human GM12878 cells, to derive a large scale picture of nuclear architecture. We find that the intensity of intra-chromosomal interactions is power-law distributed. Inter-chromosomal interactions are two orders of magnitude weaker and exponentially distributed, yet they are not randomly arranged along the genomic sequence. Intra-chromosomal contacts broadly occur between epigenomically homologous regions, whereas inter-chromosomal contacts are especially associated with regions rich in highly expressed genes. Overall, genomic contacts in the nucleus appear to be structured as a network of networks where a set of strongly individual chromosomal units, as envisaged in the 'chromosomal territory' scenario derived from microscopy, interact with each other via on average weaker, yet far from random and functionally important interactions.