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Fractality and the small-world effect in Sierpiński graphs. (Spanish) Zbl 1194.05143

Martínez Moro, Edgar (ed.), V jornadas de matemática discreta y algorítmica. Valladolid: Universidade de Valladolid, Secretariado de Publicaciones e Intercambio Editorial (ISBN 978-84-8448-380-9/pbk). Ciencias (Valladolid) 23, 117-124 (2006).
Summary: In this paper we relate fractality with the small world effect. As an example we use the family of the Sierpinski graphs. We give basic properties of these graphs and calculate their fractal dimension using the box counting method. Furthermore we define a certain family of graphs which we call the Sierpinski small world graphs. These graphs retain the fractal dimension of the Sierpinski graphs and at the same time present the small world effect.
For the entire collection see [Zbl 1123.00007].

MSC:

05C82 Small world graphs, complex networks (graph-theoretic aspects)
28A80 Fractals
91D30 Social networks; opinion dynamics
94C99 Circuits, networks
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