Eccentricity of networks with structural constraints

Abstract

The eccentricity of a node v in a network is the maximum distance from v to any other node. In social networks, the reciprocal of eccentricity is used as a measure of the importance of a node within a network. The associated centralization measure then calculates the degree to which a network is dominated by a particular node. In this work, we determine the maximum value of eccentricity centralization as well as the most centralized networks for various classes of networks including the families of bipartite networks (twomode data) with given partition sizes and tree networks with fixed number of nodes and fixed maximum degree. To this end, we introduce and study a new way of enumerating the nodes of a tree which might be of independent interest.

Centre including eccentricity algorithm for complex networks

“…To solve the above‐mentioned vulnerabilities we consider eccentricity of the nodes as a parameter. We determine the eccentricity $$e(v)$$ of the node $$v$$ in a connected network $$G$$ according to formula (2) [14]. $$\begin{eqnarray} e(v)={\rm max}\lbrace d(v,u|u \in V(G))\rbrace .$$…”

“…This method, which we named centre including eccentricity algorithm (CIEA), is more stable than the RS, CBB and GC methods and does not require updates of the excluded mass like in the MEMB method. To circumvent the vulnerabilities of the above-mentioned methods we include eccentricity used in graph theory as a parameter [14].…”

Network Analysis of Local Gene Regulators in Arabidopsis thaliana under Spaceflight Stress

“…Eccentricity: Eccentricity is a measure of the maximum distance by which a node can be connected to another node [32]. Eccentricity shows how one node is indirectly connected to other nodes in the network in the path to its target node.…”

“…As discussed in [32], the higher the eccentricity of the node, the greater is its connections with other nodes in the network. The center of the network tends to have minimum eccentricity for all nodes.…”

Exploring the Topological Characteristics of Complex Public Transportation Networks: Focus on Variations in Both Single and Integrated Systems in the Seoul Metropolitan Area

“…In this paper, we used a weighted network, where each link has a weight expressed in terms of the inversed distance between two stations connected by a common link. Hence, in order to identify the effect of distances and connections on station importance (in terms of degree), the weighted degree or station strength was analyzed by summing the weights of the links incident to the station in question [27,30,[68][69][70][71]. For station i, its weighted degree s i = N l a ij w ij is a measure of how strong and directly connected it is in a network.…”