Statistical theory of connectivity I: basic definitions and properties

Abstract

We introduce a new definition of connectivity which measures cohesion in graphs in a way which satisfies our intuitive concepts about connectivity of graphs. Several basic properties of the definition are proved including the result that spanning subgraphs of graphs have smaller cohesion than the original graph. Two component graphs are discussed and sharp lower bounds are given for connectivity as well as a differential equation whose solution yields the connectivity. © 1975.