In this paper, we review recent developments in network analysis using the graph theory, and introduce ongoing research area with relevant theoretical results. In specific, we introduce basic notations in graph, and conditional and marginal approach in constructing the adjacency matrix. Also, we introduce the Marcenko-Pastur law, the Tracy-Widom law, the white Wishart distribution, and the spiked distribution. Finally, we mention the relationship between degrees and eigenvalues for the detection of hubs in a network.