## Who doesn’t like more bandwidth?

http://news.mit.edu/2013/new-approach-to-vertex-connectivity-could-maximize-networks-bandwidth-1224

Helen Knight, an MIT news correspondent, delves into some exciting research conducted by Computer Science Graduate student, Mohsen Ghaffari, at MIT. The focus of the research was on vertex connectivity within graphs, a topic that has not been robustly researched before, marking this recent discovery both exciting to the scientific community and to those people out there who enjoy faster network capabilities.

Ghaffari and his team utilized the connectivity within graphs, to allow for simultaneous data flow within them. This new technique, would essentially maximize the data per unit of time possible to achieve with current technology. The researchers achieved this breakthrough, as mentioned above, by analyzing the connectivity of vertices. But what exactly is vertex connectivity and why is it important? As Knight put it, the vertex connectivity number is simply “how many lines or nodes would have to be removed from a given graph to disconnect it.” In other words, how quickly can the graph be broken up into components.

The reason that vertex connectivity is so important, has to do with a positive correlation between the vertex connectivity number and the number of disjoint spanning trees that can exist in the graph. The larger the vertex connectivity number, the more disjoint spanning trees may exist. These disjoint spanning trees are what allow for the simultaneous flow of data through the network, and so by optimizing the number of disjoint spanning trees that form within the network, the faster the bandwidth of that network will become.

Knight, Helen. “New Approach to Vertex Connectivity Could Maximize Networks’ Bandwidth.” *MIT News*. MIT, 24 Dec. 2013. Web. 30 Aug. 2016.