Hubs-biased resistance distances on graphs and networks

New Resistance Distances with Global Information on Large Graphs

We consider the problem that on large random geometric graphs, random walk-based distances between nodes do not carry global information such as cluster structure. Instead, as the graphs become larger, the distances contain mainly the obsolete information of local density of the nodes. Many distances or similarity measures between nodes on a graph have been proposed but none are both proved to ...

Resistance distances and the Kirchhoff index in Cayley graphs

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, closed-form formulae for the Kirchhoff index and resistance distances of the Cayley graphs ov...

Regions, Distances and Graphs

Avoir deux directeurs de thèse, c'est avant tout une richesse et une opportunité d'apprendre deux fois plus. Cela permet d'avoir deux points de vue, et cela forcè a faire ses propres choix. J'ai eu cepriviì ege. Aussi je voudrais remercier Jean et Stefan. D'abord pour m'avoir guidé, con-seillé, motivé; et pour avoir passé tout ce tempsà relire et corriger mes travaux. Mais aussi, et surtout, po...

Biased Graphs

On strong distances in oriented graphs

Let D be a strongly connected digraph. The strong distance between two vertices u and v in D, denoted by sdD(u; v) is the minimum size of a strongly connected subdigraph of D containing u and v. The strong eccentricity, se(u), of a vertex u of D, is the strong distance between u and a vertex farthest from u. The minimum strong eccentricity among the vertices of D is the strong radius, srad(D), ...