Criado Herrero, ReginoGarcía, EstherPedroche Sánchez, FranciscoRomance, Miguel2017-05-112017-05-112016-01-010377-0427https://riunet.upv.es/handle/10251/80984In this paper we analyze families of rankings by studying structural properties of graphs. Given a finite number of elements and a set of rankings of those elements, two elements compete when they exchange their relative positions in at least two rankings, and we can associate an undirected graph to a set of rankings by connecting elements that compete. We call this graph a competitivity graph. Competitivity graphs have already appeared in the literature as co-comparability graphs, f-graphs or intersection graphs associated to a concatenation of permutation diagrams. We introduce certain important sets of nodes in a competitivity graph. For example, nodes that compete among them form a competitivity set and nodes connected by chains of competitors form a set of eventual competitors. These sets are analyzed and a method to obtain sets of eventual competitors directly from a set of rankings is shown. © 2015 Elsevier B.V.Reserva de todos los derechosGraphic methodsComparability graphsCompetitivityFinite numberIntersection graphPermutation graphRelative positionsUndirected graphGraph theoryMATEMATICA APLICADAArtículo10.1016/j.cam.2015.03.009Abierto