The idea that structural white matter connectivity constrains functional connectivity (interactions among brain regions) has widely been explored in studies of brain networks; studies have mostly focused on the "average" strength of functional connectivity. The question of how structural connectivity constrains the "variability" of functional connectivity remains unresolved. In this study, we i...

High spatial and angular resolution diffusion weighted imaging (DWI) with network analysis provides a unique framework for the study of brain structure in vivo. DWI-derived brain connectivity patterns are best characterized with graph theory using an edge weight to quantify the strength of white matter connections between gray matter nodes. Here a dimensionless, scale-invariant edge weight is i...

We consider the problem of maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding. We describe algorithms and data structures for maintaining information about 2and 3-vertex-connectivity, and 3and 4-edge-connectivity in a planar graph in O(n1/2) amortized time per insertion, deletion, or connectivity query. All ...

As a generalization of the traditional connectivity, g -component edge connectivity c ? ( G ) non-complete graph is minimum number edges to be deleted from such that resulting has at least components. Hypercube-like networks (HL-networks for short) are obtained by manipulating some pairs in hypercubes, which contain several famous interconnection as twisted cubes, Möbius crossed locally cubes. ...

Graph Connectivity and Network Coding LEUNG, Kai Man Master of Philosophy Department of Computer Science and Engineering The Chinese University of Hong Kong 2011 In this thesis we present a new algebraic formulation to compute edge connectivities in a directed graph, using the ideas developed in network coding. This reduces the problem of computing edge connectivities to solving systems of line...