Scan Statistics for Interstate Alliance Graphs

In this paper we discuss work on graphs defined in terms of alliances between countries. We will use scan statistics to investigate years in which there are an unusual number of agreements, not just between one country and its allies, but amongst the allies themselves. This is related to work on email “chatter” discussed in Priebe et al. [2006]. In this section we will lay out the basic graph terminology. A graph G is a pair (V, E) where V is a set (the vertices) and E is a set of unordered pairs of elements of V (the edges). We call the order of the graph n = |V | and the size of the graph s = |E|. See Bollobás [2001]. We will denote the edge from v to w as vw For v, w ∈ V the distance d(v, w) is defined to be the minimum path length from v to w in E. The (closed) kth-order neighborhood (or k-neighborhood) of a vertex v is the set of vertices of distance at most k from v: Nk(v) = {w ∈ V : d(v, w) ≤ k}.