Graph wavelet applied to human brain connectivity

The graph theory is increasingly used and provides powerful tools for studying complex biological networks problems. They were able to characterize the small-worldness of the brain connectivity network and were accurate enough to observe topological differences between healthy and diseased brain graphs. However, these methods relied on topological characteristics implying that differences could be observed between two groups only if corresponding graphs topologies were different. In this paper, we developed a multiscale method to characterize fine to coarse brain connectivity, which allows to observe connectivity differences between two groups even if corresponding graphs topologies are identical. For this purpose, we defined a new wavelet graph transform based on the interval wavelet transform. Our method decomposes the connectivity values of a graph regardless of its topology, can be defined with a large spectrum of wavelet bases and is invertible. Finally, we applied our graph wavelet decomposition on brain connectivity graph in a group of healthy controls.