WebThe four-point Steiner distance is the minimum of the total geodesic distances within the metric space from four given points to a point. For Vicsek networks, we obtain the asymptotic formula of their mean Steiner distances using the method of finite pattern. Publication: Fractals Pub Date: 2024 DOI: 10.1142/S0218348X21502613 Bibcode: WebFeb 15, 2024 · In the classical Vicsek model, it was found that the emergence of self-ordered motion in systems of particles when the direction of each particles’ motion of at the next moment is updated according to its all neighbors’ mean direction.

Weighted average geodesic distance of Vicsek network

WebMar 24, 2008 · In this paper, the exact formula for the mean geodesic distance of Vicsek fractals is found. The quantity is computed precisely through the recurrence relations derived from the self-similar structure of the fractals considered. WebThe topological indexes, such as the Wiener sum and the eccentric distance sum, play important roles in Chemical Graph Theory, where the eccentric distance sum characterizes the geodesic distance of two nodes. In this paper, for a family of self-similar Vicsek networks, we discuss their eccentric distance sums related to the Steiner distance of four … days of the week to addams family tune

Weighted average geodesic distance of Vicsek network in three ...

WebAbstract The Fermat point of a triangle is a point that the total distance from the three vertices of the triangle to the point is the minimum possible. Considering the Fermat problem within a network, we study the average Fermat distance of three random nodes on the Vicsek networks by using the method of finite pattern. Keywords: Fractal Network WebJun 2, 2024 · J. Phys. A: Math. Theor. 41 (2008) 485102 Z Zhang et al The paths that contribute to t must all go through at least one of the 2f edge nodes (such as G,X,Y and Z in figure 2) at which the different V f,t branches are connected. The analytical expression for t, named the crossing path length [9], can be derived as below. Denote α,β t as the sum of … WebAbstract: The hyper-Wiener index is an important topological invariant, which is based on the distance between two vertexes on a graph. This paper is concerned with the hyper-Wiener indices of Vicsek networks. Based on the method of finite pattern, we calculate the asymptotic formula of the hyper-Wiener indices of Vicsek networks. days of the week to addams family