Human brain is a very complex system. It has many operational units, which work in synergy to help us accomplish different tasks. In this thesis we have looked into one of such task which is the retrieval of words in speech production. This seemingly simple task of word selection while we speak involves a large number of regions interacting with one another. We have used graph learning technique of graph signal processing (GSP), to find a map of these regional interactions called functional brain connectivity. This connectivity map is found by analysing the electrocorticographic (ECoG) data collected from 5 subjects. The subjects were asked to perform a cyclic picture naming task. This task consists of naming the pictures in semantically homogeneous and heterogeneous blocks. It has been observed that word retrieval is hindered while repeatedly naming pictures in semantically homogeneous block. This effect is called as semantic interference effect. The graph learning method infers the brain connectivity based on the smoothness of the signal present on the graph. This is achieved by solving a joint optimization problem for noiseless version of the signal on the graph and a corresponding graph Laplacian matrix. This graph Laplacian matrix is then used to find the adjacency matrices of the graph which represent the functional brain connectivity. In this research we found that the during word retrieval frontal and temporal regions of the brain functionally connected with each other. We also found many intra-lobe connections supporting word retrieval. Another interesting result from this research shows that the density of the functional connectivity map is higher in case of word selection when compared to lexical access. This means that the process of word selection is more complex and requires more support from multiple regions of the brain.