2016/08/07 by C. Dalfó, M.A. Fiol, Dalfó, C. +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #05C12 #05C82 #05C85 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Gene Regulatory Network Analysis #Neural Networks Stability and Synchronization
paper · pdf · doi:10.48550/arxiv.1608.02197
openalex publication_date 2016/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of the models are based on stochastic methods, some deterministic constructions have been recently proposed, because this allows a better computation of their properties. Here a new deterministic family of hierarchical networks is presented, which generalizes most of the previous proposals, such as the so-called binomial tree. The obtained graphs can be seen as graphs on alphabets (where vertices are labeled with words of a given alphabet, and the edges are defined by a specific rule relating different words). This allows us the characterization of their main distance-related parameters, such as the radius and the diameter. Moreover, as a by product, an efficient shortest-path local algorithm is proposed.