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One of the most characteristic features of biological molecular networks is that the network structure itself changes, depending on the cellular environment. Indeed, activated molecules show a variety of responses to distinctive cell conditions, and subsequently the network structures of active molecules also change. Here we present an approach to trace the network structure changes by using the graphical chain model developed from the gene expression data. The previous procedure for applying the graphical chain model to the expression profiles of a limited number of genes has been improved to analyze the entire set of genes. Furthermore, the chain model has been rearranged according to the association strength, and was scrutinized to identify the candidates of essential gene-gene relationships for the network changes, by using the path consistency algorithm. The improved procedure was applied to the expression profiles of 8,427 genes, which were measured in two distinctive stages of liver cancer progression. As a result, the chain model of the 18 gene cluster relationships with strong associations was inferred, in which the coordination of clusters was described in the cell stage progression, and the gene-gene relationships between known cancer-related genes causing the progression were further refined. Thus, the present procedure is a useful method to model the network structure changes in the cell stage progression, and to clarify the gene candidates for the progression.