Graph Convolutional Networks (GCN) have been effective at tasks that have rich relational structure and can preserve global structure information of a dataset in graph embeddings. Recently, many researchers focused on examining whether GCNs could handle different Natural Language Processing tasks, especially text classification. While applying GCNs to text classification is well-studied, its graph construction techniques, such as node/edge selection and their feature representation, and the optimal GCN learning mechanism in text classification is rather neglected. In this paper, we conduct a comprehensive analysis of the role of node and edge embeddings in a graph and its GCN learning techniques in text classification. Our analysis is the first of its kind and provides useful insights into the importance of each graph node/edge construction mechanism when applied at the GCN training/testing in different text classification benchmarks, as well as under its semi-supervised environment.