000058365 001__ 58365
000058365 005__ 20170327111841.0
000058365 0247_ $$2doi$$a10.1063/1.4896332
000058365 0248_ $$2sideral$$a87957
000058365 037__ $$aART-2014-87957
000058365 041__ $$aeng
000058365 100__ $$aLacasa, L.
000058365 245__ $$aAnalytical estimation of the correlation dimension of integer lattices
000058365 260__ $$c2014
000058365 5060_ $$aAccess copy available to the general public$$fUnrestricted
000058365 5203_ $$aIn this article we address the concept of correlation dimension which has been recently extended to network theory in order to eciently characterize and estimate the dimensionality and geometry of complex networks [1]. This extension is inspired in the Grassberger-Procaccia method [2{4], originally designed to quantify the fractal dimension of strange attractors in dissipative chaotic dynamical systems. When applied to networks, it proceeds by capturing the trajectory of a random walker di using over a network with well de ned dimensionality. From this trajectory, an estimation of the network correlation dimension is retrieved by looking at the scaling of the walker's correlation integral. Here we give analytical support to this methodology by obtaining the correlation dimension of synthetic networks representing well-de ned limits of real networks. In particular, we explore fully connected networks and integer lattices, these latter being coarsely-equivalent [20] to Euclidean spaces. We show that their correlation dimension coincides with the the Haussdor dimension of the respective coarsely-equivalent Euclidean space.
000058365 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000058365 590__ $$a1.954$$b2014
000058365 591__ $$aPHYSICS, MATHEMATICAL$$b9 / 54 = 0.167$$c2014$$dQ1$$eT1
000058365 591__ $$aMATHEMATICS, APPLIED$$b17 / 255 = 0.067$$c2014$$dQ1$$eT1
000058365 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000058365 700__ $$0(orcid)0000-0002-3484-6413$$aGómez-Gardeñes, J.$$uUniversidad de Zaragoza
000058365 7102_ $$12003$$2395$$aUniversidad de Zaragoza$$bDepartamento de Física de la Materia Condensada$$cFísica de la Materia Condensada
000058365 773__ $$g24, 4 (2014), [6 pp]$$pChaos$$tCHAOS$$x1054-1500
000058365 8564_ $$s358655$$uhttps://zaguan.unizar.es/record/58365/files/texto_completo.pdf$$yVersión publicada
000058365 8564_ $$s122675$$uhttps://zaguan.unizar.es/record/58365/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000058365 909CO $$ooai:zaguan.unizar.es:58365$$particulos$$pdriver
000058365 951__ $$a2016-12-21-12:49:49
000058365 980__ $$aARTICLE