The parameter of distance plays an important role in studying the properties symmetric networks such as connectedness, diameter, vertex centrality and complexity. Particularly different metric-based fractional models are used diverse fields computer science integer programming, pattern recognition, robot navigation. In this manuscript, we have computed all local resolving neighborhood sets esta...

We propose Diffusion Centrality (DC) in which semantic aspects of a social network are used to characterize vertices that are influential in diffusing a property p. In contrast to classical centrality measures, diffusion centrality of vertices varies with the property p, and depends on the diffusion model describing how p spreads. We show that DC applies to most known diffusion models including...

For a clutter C over ground set E, a pair of distinct edges e, f ∈ E are coexclusive if every minimal cover contains at most one of them. An identification of C is another clutter obtained after identifying coexclusive edges of C. If a clutter is non-packing, then so is any identification of it. Inspired by this observation, and impelled by the lack of a qualitative characterization for ideal m...

Centrality measures, erstwhile popular amongst the sociologists and psychologists, have seen broad and increasing applications across several disciplines of late. Amongst a plethora of application specific definitions available in the literature to rank the vertices, closeness centrality, betweenness centrality and eigenvector centrality (page-rank) have been the most important and widely appli...

We present a simple linear time combinatorial algorithm for the Betweenness problem. In the Betweenness problem, we are given a set of vertices and betweenness constraints. Each betweenness constraint of the form x {y, z} requires that vertex x lies between vertices y and z. Our goal is to find a linear ordering of vertices that maximizes the number of satisfied constraints. In 1995, Chor and S...

Force-directed layout algorithms produce graph drawings by resolving a system of emulated physical forces. We present techniques for using social gravity as an additional force in force-directed layouts, together with a scaling technique, to produce drawings of trees and forests, as well as more complex social networks. Social gravity assigns mass to vertices in proportion to their network cent...

Graph robustness or network is the ability that a graph preserves its connectivity other properties after loss of vertices and edges, which has been central problem in research complex networks. In this paper, we introduce Modified Zagreb index centrality as novel measures to study robustness. We theoretically find some relationships between these measures. Then, use analyze BA scale-free netwo...

let g be a graph with p vertices and q edges and a = {0, 1, 2, . . . , [q/2]}. a vertex labeling f : v (g) → a induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. for a ∈ a, let vf (a) be the number of vertices v with f(v) = a. a graph g is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in a, |vf (a) − vf (b)| ≤ 1 and the in...

The induced path interval J (u; v) consists of the vertices on the induced paths between u and v in a connected graph G. Di-erences in properties with the geodesic interval are studied. Those graphs are characterized, in which the induced path intervals de/ne a proper betweenness. The intersection of the induced path intervals between the pairs of a triple, in general, consists of a big chunk o...

This paper presents a new algorithm for correcting incorrect line drawings—incorrect projections of a polyhedral scene. Such incorrect drawings arise, e.g., when an image of a polyhedral world is taken, the edges and vertices are extracted, and a drawing is synthesized. Along the way, the true positions of the vertices in the 2D projection are perturbed due to digitization errors and the prepro...