Abstract We examine the eigenvalue spectrum, ρ(μ), of the adjacency matrix of a random scale-free network with an average of p edges per vertex using the replica method. We show how in the dense limit, when p → ∞, one can obtain two relatively simple coupled equations whose solution yields ρ(μ) for an arbitrary complex network. For scale-free graphs, with degree distribution exponent λ, we obta...

PURPOSE To study the relationship between cone spacing and density and clinical measures of visual function near the fovea. METHODS High-resolution images of the photoreceptor mosaic were obtained with adaptive optics scanning laser ophthalmoscopy from 26 patients with inherited retinal degenerations. Cone spacing measures were made close to or at the foveal center (mean [SD] eccentricity, 0....

For a vertex v and a (k−1)-element subset P of vertices of a graph, one can define the distance from v to P in various ways, including the minimum, average, and maximum distance from v to P . Associated with each of these distances, one can define the keccentricity of the vertex v as the maximum distance over all P , and the k-eccentricity of the set P as the maximum distance over all v. If k =...

PURPOSE To determine the values in decibels of retinal sensitivity within the central 26 degrees of the visual field of normal subjects divided into homogenous age groups using the Octopus 1-2-3; to compare the values of retinal sensitivity we have found with those considered normal in the statistical package obtained by a multicenter study performed in 1994 with Octopus 201. METHODS 181 subj...

The eccentricity connectivity index of a molecular graph G is defined as (G) = aV(G) deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to other vertices of G and deg(a) is degree of vertex a. Here, we compute this topological index for some infinite classes of dendrimer graphs.

Studies have shown that spatial aftereffects increase with eccentricity. Here, we demonstrate that the shape-frequency and shape-amplitude aftereffects, which describe the perceived shifts in the shape of a sinusoidal-shaped contour following adaptation to a slightly different sinusoidal-shaped contour, also increase with eccentricity. Why does this happen? We first demonstrate that the percept...

The eccentricity of a vertex is the maximum distance from it to another vertex, and the average eccentricity of a graph is the mean eccentricity of a vertex. In this paper we introduce average edge and average vertex-edge mean eccentricities of a graph. Moreover, relations among these eccentricities for trees are provided as well as formulas for line graphs and cartesian product of graphs. In t...

Distance-based indices, including closeness centrality, average path length, eccentricity and average eccentricity, are important tools for network analysis. In these indices, the distance between two vertices is measured by the size of shortest paths between them. However, this measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs (and also directed g...

Scale free graphs can be found very often as models of real networks and are characterized by a power law degree distribution, that is, for a constant γ ≥ 1 the number of vertices of degree d is proportional to d−γ . Experimental studies show that the eigenvalue distribution also follows a power law for the highest eigenvalues. Hence it has been conjectured that the power law of the degrees det...