3,393 research outputs found

    Resistance distance, information centrality, node vulnerability and vibrations in complex networks

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    We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability.We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality

    Inverse Problems Related to the Wiener and Steiner-Wiener Indices

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    In a graph, the generalized distance between multiple vertices is the minimum number of edges in a connected subgraph that contains these vertices. When we consider such distances between all subsets of kk vertices and take the sum, it is called the Steiner kk-Wiener index and has important applications in Chemical Graph Theory. In this thesis we consider the inverse problems related to the Steiner Wiener index, i.e. for what positive integers is there a graph with Steiner Wiener index of that value

    Wiener Index and Remoteness in Triangulations and Quadrangulations

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    Let GG be a a connected graph. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. We provide asymptotic formulae for the maximum Wiener index of simple triangulations and quadrangulations with given connectivity, as the order increases, and make conjectures for the extremal triangulations and quadrangulations based on computational evidence. If σ(v)\overline{\sigma}(v) denotes the arithmetic mean of the distances from vv to all other vertices of GG, then the remoteness of GG is defined as the largest value of σ(v)\overline{\sigma}(v) over all vertices vv of GG. We give sharp upper bounds on the remoteness of simple triangulations and quadrangulations of given order and connectivity
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