Traditional depression research based on electroencephalogram (EEG) regards electrodes as isolated nodes and ignores the correlation between them. So it is difficult to discover abnormal brain topology alters in patients with depression. To resolve this problem, this paper proposes a framework for depression recognition based on brain function network (BFN). To avoid the volume conductor effect, the phase lag index is used to construct BFN. BFN indexes closely related to the characteristics of “small world” and specific brain regions of minimum spanning tree were selected based on the information complementarity of weighted and binary BFN and then potential biomarkers of depression recognition are found based on the progressive index analysis strategy. The resting state EEG data of 48 subjects was used to verify this scheme. The results showed that the synchronization between groups was significantly changed in the left temporal, right parietal occipital and right frontal, the shortest path length and clustering coefficient of weighted BFN, the leaf scores of left temporal and right frontal and the diameter of right parietal occipital of binary BFN were correlated with patient health questionnaire 9-items (PHQ-9), and the highest recognition rate was 94.11%. In addition, the study found that compared with healthy controls, the information processing ability of patients with depression reduced significantly. The results of this study provide a new idea for the construction and analysis of BFN and a new method for exploring the potential markers of depression recognition.