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It is known that many networks modeling real-life complex systems aresmall-word (large local clustering and small diameter) and scale-free (powerlaw of the degree distribution), and very often they are also hierarchical.Although most of the models are based on stochastic methods, some deterministicconstructions have been recently proposed, because this allows a bettercomputation of their properties. Here a new deterministic family ofhierarchical networks is presented, which generalizes most of the previousproposals, such as the so-called binomial tree. The obtained graphs can be seenas graphs on alphabets (where vertices are labeled with words of a givenalphabet, and the edges are defined by a specific rule relating differentwords). This allows us the characterization of their main distance-relatedparameters, such as the radius and the diameter. Moreover, as a by product, anefficient shortest-path local algorithm is proposed.

A new general family of deterministic hierarchical networks