Recently, modular organization of intrinsic brain networks has been revealed by the graph theoretical analysis of resting-state functional MRI (rs-fMRI). In this paper, we introduce the concept of the graph theoretical analysis and modular organization. Then, we present the results of our analysis. In the graph theoretical analysis, intrinsic brain networks measured by rs-fMRI are modeled as the graphs (nodes linked by edges). Then, a module is defined as a group of highly inter-connected nodes which have relatively sparse connections to nodes in other modules. Recently, effective module detection methods have been proposed, and applied to rs-fMRI. In our study, rs-fMRI data were collected from 18 healthy young participants, and we detected the modules from a group level graph with fine spatial resolution. As a result, we found 6 dominant modules (default-mode, fronto-parietal, cingulo-opercular, sensorimotor, visual, and auditory). These modules were also detected when another module detection method was applied. Then, nodes were classified according to their roles based on their intra-module and inter-module connections. We found that majority of brain regions were classified as peripheral nodes which mostly connect with nodes within their modules. Interestingly, fronto-parietal module which consists of transmodal higher-order brain regions had more connector nodes (connecting with other modules) than unimodal visual and sensorimotor modules. This suggested that modular organization in intrinsic brain networks can reflect functional properties of brain systems.