Mobile sensor networks rely heavily on inter-sensor connectivity for collection of data. Nodes in these networks monitor different regions of an area of interest and collectively present a global overview of some monitored activities or phenomena. A failure of a sensor leads to loss of connectivity and may cause partitioning of the network into disjoint segments. A number of approaches have be...

Regional connectivity measurements derived from diffusion imaging datasets are of considerable interest in the neuroimaging community for better understanding white matter connectivity. Current connectivity measurements are usually either based on fiber tractography applied in Monte-Carlo fashion, or variations of the Hamilton-Jacobi approach, or are graph-based. We propose a novel, graph-based...

We initiate the study of k -edge-connected orientations undirected graphs through edge flips for ≥ 2. prove that in every orientation an 2k graph, there exists a sequence edges such flipping their directions one by does not decrease connectivity, and final is -edge connected. This yields “edge-flip based” new proof Nash-Williams’ theorem: A graph G has if only As another consequence theorem, we...