We show that a random labeled n-vertex graph almost surely contains isomorphic copies of almost all labeled n-vertex trees, in two senses. In the first sense, the probability of each edge occurring in the graph diminishes as n increases, and the set of trees referred to as "almost all" depends on the random graph. In the other sense, the probability of an edge occurring is fixed, and the releva...

It is known that humans form non-transitive preferences. We propose to model human preferences as a complete weighted directed graph where nodes are objects of preference, and an edge leading from one node to another has weight equal to the probability that the destination node will be preferred (or chosen) from the pair connected by the edge. We also propose that the most preferred object(s) m...

A novel method for edge detection in vector images is proposed that does not require any prior knowledge of the imaged scenes. In the derivation, it is assumed that the observed vector images are realizations of spatially quasistationary processes, and that the vector observations are generated by parametric probability distribution functions of known form whose parameters are in general unknow...

Though our main technical result concerns random graphs in the G(n,p) model, let us mention other contexts in which threshold phenomena occur. One classical example is Percolation, an area started in physics. A typical question here is this: given a planar grid and 0 < p < 1. Create a graph by keeping each edge of the planar grid with probability p and removing each edge with probability 1-p. T...

A random bipartite graph G n n p is obtained by taking two disjoint subsets of vertices A and B of cardinality n each, and by connecting each pair of vertices a ! A and b ! B by an edge randomly and independently with probability p " p n . We show that the choice number of G n n p is, almost surely, 1 # o 1 log2 np for all values of the edge probability p " p n , where the o 1 term tends to 0 a...

This paper evaluates the performance of edge-based directional probability distributions as features in writer identification in comparison to a number of non-angular features. It is noted that the joint probability distribution of the angle combination of two ”hinged” edge fragments outperforms all other individual features. Combining features may improve the performance. Limitations of the me...

We propose a new random graph model—Edge Popularity—for the web graph and other complex networks, where edges are deleted over time and an edge is chosen to be deleted with probability inversely proportional to the in-degree of the destination. We show that with probability tending to one as time tends to infinity, the model generates graphs whose degree distribution follows a power law. Depend...

‎let $g=(v(g),e(g))$ be a simple connected graph with vertex set $v(g)$ and edge‎ ‎set $e(g)$‎. ‎the (first) edge-hyper wiener index of the graph $g$ is defined as‎: ‎$$ww_{e}(g)=sum_{{f,g}subseteq e(g)}(d_{e}(f,g|g)+d_{e}^{2}(f,g|g))=frac{1}{2}sum_{fin e(g)}(d_{e}(f|g)+d^{2}_{e}(f|g)),$$‎ ‎where $d_{e}(f,g|g)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $e(g)$ and $d_{e}(f|g)=s...

Percolation with edge-passage probability p and first-passage percolation are studied for the n-cube Bn = {0, 1} with nearest neighbor edges. For oriented and unoriented percolation, p = e/n and p = 1/n are the respective critical probabilities. For oriented first-passage percolation with i.i.d. edge-passage times having a density of 1 near the origin, the percolation time (time to reach the op...