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Recently, the concept of mutual information has been proposed for inferring the structure of genetic regulatory networks from gene expression profiling. After analyzing the limitations of mutual information in inferring the gene-to-gene interactions, this paper introduces the concept of conditional mutual information and, based on this, proposes two novel algorithms to infer the connectivity structure of genetic regulatory networks. One of the proposed algorithms exhibits a better accuracy, whereas the other algorithm excels in simplicity and flexibility. By exploiting the mutual information and conditional mutual information, a practical metric is also proposed to assess the likeliness of direct connectivity between genes. This novel metric resolves a common limitation associated with the current inference algorithms, namely, the situations where the gene connectivity is established in terms of the dichotomy of being either connected or disconnected. Based on the data sets generated by synthetic networks, the performance of the proposed algorithms is compared favorably relative to existing state-of-the-art schemes. The proposed algorithms are also applied on realistic biological measurements such as the cutaneous melanoma data set, and biological meaningful results are inferred.