The prediction of depression is a crucial area of research which makes it one of the top priorities in mental health research as it enables early intervention and can lead to higher success rates in treatment. Self-reported feelings by patients represent a valuable biomarker for predicting depression as they can be expressed in a lower-dimensional network form, offering an advantage in visualizing the interactive characteristics of depression-related feelings. Furthermore, the network form of data expresses high-dimensional data in a compact form, making the data easy to use as input for the machine learning processes. In this study, we applied the graph convolutional network (GCN) algorithm, an effective machine learning tool for handling network data, to predict depression-prone patients using the network form of self-reported log data as the input. We took a data augmentation step to expand the initially small dataset and fed the resulting data into the GCN algorithm, which achieved a high level of accuracy from 86-97% and an F1 (harmonic mean of precision and recall) score of 0.83-0.94 through three experimental cases. In these cases, the ratio of depressive cases varied, and high accuracy and F1 scores were observed in all three cases. This study not only demonstrates the potential for predicting depression-prone patients using self-reported logs as a biomarker in advance, but also shows promise in handling small data sets in the prediction, which is critical given the challenge of obtaining large datasets for biomarker research. The combination of self-reported logs and the GCN algorithm is a promising approach for predicting depression and warrants further investigation.