Node betweenness has been studied recently by a number of authors, but until now less attention has been paid to edge betweenness. In this paper, we present an exact analytic study of edge betweenness in evolving scale-free and non-scale-free trees. We aim at the probability distribution of edge betweenness under the condition that a local property, the in-degree of the "younger" node of a rand...

In the Perfect Completion problem one wishes to add the fewest possible edges to a graph in order to obtain a perfect graph. How large can the size of the added edge set be compared to the size of the edge set of the original graph? We show that with high probability the smallest perfect graph containing a random graph G(n; n 0:6) has (n 1:8) edges. We also show that with high probability the m...

This chapter evaluates the performance of edge-based directional probability distributions as features in writer identification in comparison to a number of other texture-level features encoding non-angular information. We introduce here a new feature: the joint probability distribution of the angle combination of two ”hinged” edge fragments. It is noted that the ”edge-hinge” distribution outpe...

Let p,s 2 ð0,1 with s4p, let m,n 2 N with 1omon, and define V={1,y,n}. Let ER(n,p) denote the random graph model on V where each edge is independently included in the graph with probability p. Let kðn,p,m,sÞ denote the random graph model on V where each edge among the m vertices {1,y,m} is independently included in the graph with probability s and all other edges are independently included with...

1. Let G = (V,E) be a c-edge connected graph. In other words, assume that the size of minimum cut in G is at least c. Construct a graph G′(V,E ′) by sampling each edge of G with probability p independently at random and reweighing each edge with weight 1/p. Suppose c > log n, and is such that 10 log(n) c 2 ≤ 1. Show that as long as p ≥ 10 log(n) c 2 , with high probability the size of every cut...

In this paper we examine the reliability properties of the ideal fat-tree, a general model used to capture both distance and bandwidth constraints of various classes of fat-tree networks. We use the notion (see NPSY94]) of a random graph of type?G obtained by selecting edges of a given undirected graph G independently and with probability p, thus representing a network in which links fail indep...

We examine the relationship of a graph G and its random subgraphs which are defined by independently choosing each edge with probability p. Suppose that G has a spectral gap λ (in terms of its normalized Laplacian) and minimum degree dmin. Then we can show that a random subgraph of G on n vertices with edge-selection probability p almost surely has as its spectral gap λ−O (√ logn pdmin + (logn)...

Effects of the electron-electron interaction on tunneling in a semiconductor nanowhisker are studied in a magnetic quantum limit. We consider the system with which bulk and edge states coexist. In bulk states, the temperature dependence of the transmission probability is qualitatively similar to that of a one-dimensional electron system. We investigate contributions of edge states on transmissi...