Vertex labeling and routing in expanded Apollonian networks

We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their nodes that allows one to determine a shortest path routing between any two nodes of the network based only on the labels

Models deterministes de xarxes complexes

En estudis recents s'ha observat que moltes xarxes associades a sistemes complexos pertanyen a una nova categoria que s'ha volgut anomenar petit-món amb invariància d'escala. Molts dels models que s'han desenvolupat per a la descripció matemàtica d'aquestes xarxes es basen en construccions probabilístiques. Tanmateix, la consideració de models deterministes és útil per completar i millorar les tècniques probabilístiques i d'altres basades en simulacions. En aquest article introduïm els conceptes i models bàsics que s'han considerat en l'estudi de xarxes complexes i es presenten diversos models deterministes que es generen a partir de grafs complets.Recent studies have shown that a number of networks associated to complex systems belong to the new category of “scale–free small–world networks”. The mathematical description of these networks is often based in probabilistic models. However, deterministic models are useful to improve or complete the analysis of these networks obtained by probabilsitic techniques or by simulation. In this paper we introduce the concepts and basic models which have been considered to analyze complex networks and we describe several deterministic models which are obtained from complete graphs