Vulnerability of Directed Communication Nets
Instability Theorem · 1971
d+(x) be the number of arcs directed away from x (outdegree of node x), and let d-(x) be the number of arcs directed toward x (indegree of node x). Let Xc N and il= N- X and define d,+[X(x)] number of arcs directed away from XE X to nodes in x; d<+[X(x)] number of arcs directed away from XE X to nodes in X; de-[X(x)] number of arcs directed toward XE X from nodes in jz; di- [ X(x)] number of arcs directed toward XE X from nodes in X. Clearly for XE X, d+(x) = di+[ X(x)] +def[ X(x)] and d-(x) = di-IX(x)] +d,-[X(x)]. Define d+(X) =&xd,+[X(x)] and d-(X) =&x d,-[X(x)]. d+(X) is the outdegree and d-(X) is the indegree of the set of nodes X. Clearly d+(X) = d-(x) and d-(X) = d+(z).