Human brain connectivity is complex. Graph theory based analysis has become a powerful and popular approach for analyzing brain imaging data, largely because of its potential to quantitatively illuminate the networks, the static architecture in structure and function, the organization of dynamic behavior over time, and disease related brain changes. The first step in creating brain graphs is to define the nodes and edges connecting them. We review a number of approaches for defining brain nodes including fixed versus data-driven nodes. Expanding the narrow view of most studies which focus on static and/or single modality brain connectivity, we also survey advanced approaches and their performances in building dynamic and multi-modal brain graphs. We show results from both simulated and real data from healthy controls and patients with mental illnesse. We outline the advantages and challenges of these various techniques. By summarizing and inspecting recent studies which analyzed brain imaging data based on graph theory, this article provides a guide for developing new powerful tools to explore complex brain networks.

By exploiting cross-information among multiple imaging data, multimodal fusion has often been used to better understand brain diseases. However, most current fusion approaches are blind, without adopting any prior information. There is increasing interest to uncover the neurocognitive mapping of specific clinical measurements on enriched brain imaging data; hence, a supervised, goal-directed model that employs prior information as a reference to guide multimodal data fusion is much needed and becomes a natural option. Here, we proposed a fusion with reference model called "multi-site canonical correlation analysis with reference + joint-independent component analysis" (MCCAR+jICA), which can precisely identify co-varying multimodal imaging patterns closely related to the reference, such as cognitive scores. In a three-way fusion simulation, the proposed method was compared with its alternatives on multiple facets; MCCAR+jICA outperforms others with higher estimation precision and high accuracy on identifying a target component with the right correspondence. In human imaging data, working memory performance was utilized as a reference to investigate the co-varying working memory-associated brain patterns among three modalities and how they are impaired in schizophrenia. Two independent cohorts (294 and 83 subjects respectively) were used. Similar brain maps were identified between the two cohorts along with substantial overlaps in the central executive network in fMRI, salience network in sMRI, and major white matter tracts in dMRI. These regions have been linked with working memory deficits in schizophrenia in multiple reports and MCCAR+jICA further verified them in a repeatable, joint manner, demonstrating the ability of the proposed method to identify potential neuromarkers for mental disorders.