Web Communities and Connectivity in Random Graphs David Pike Abstract: Our research is motivated by the problem of identifying groups of related webpages in the World Wide Web.  We begin with the Web Graph, whereby each webpage of the WWW is represented by a vertex, and each arc represents a hyperlink from one page to another. Consider the hypothesis that two vertices, say u and v, are related to each other if there is an arc from u to v, and also an arc from v to u.  This concept can be further extended:  if we have two related vertices (u and v) such that some third vertex w has an arc to one of them and also an arc from one of them, then we will deem all three to be related. We investigate this relationship hypothesis and compare it with the notion of strong connectivity.  Our results are mostly focussed on random graphs at this point. This is joint work with Alasdair Graham.