The spatial conformation of a genome plays an important role in the long-range regulation of genome-wide gene expression and methylation, but has not been extensively studied due to lack of genome conformation data. The recently developed chromosome conformation capturing techniques such as the Hi-C method empowered by next generation sequencing can generate unbiased, large-scale, high-resolution chromosomal interaction (contact) data, providing an unprecedented opportunity to investigate the spatial structure of a genome and its applications in gene regulation, genomics, epigenetics, and cell biology. In this work, we conducted a comprehensive, large-scale computational analysis of this new stream of genome conformation data generated for three different human leukemia cells or cell lines by the Hi-C technique. We developed and applied a set of bioinformatics methods to reliably generate spatial chromosomal contacts from high-throughput sequencing data and to effectively use them to study the properties of the genome structures in one-dimension (1D) and two-dimension (2D). Our analysis demonstrates that Hi-C data can be effectively applied to study tissue-specific genome conformation, chromosome-chromosome interaction, chromosomal translocations, and spatial gene-gene interaction and regulation in a three-dimensional genome of primary tumor cells. Particularly, for the first time, we constructed genome-scale spatial gene-gene interaction network, transcription factor binding site (TFBS) - TFBS interaction network, and TFBS-gene interaction network from chromosomal contact information. Remarkably, all these networks possess the properties of scale-free modular networks.