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@Article{CasaGrandeCotaHase:2017:RaWaDe,
               author = "Casa Grande, H. L. and Cotacallapa Choque, Frank Moshe and Hase, 
                         M. O.",
          affiliation = "{Universidade de S{\~a}o Paulo (USP)} and {Instituto Nacional de 
                         Pesquisas Espaciais (INPE)} and {Universidade de S{\~a}o Paulo 
                         (USP)}",
                title = "Random walk in degree space and the time-dependent Watts-Strogatz 
                         model",
              journal = "Physical Review E",
                 year = "2017",
               volume = "95",
               number = "1",
                pages = "012321",
                month = "Jan.",
             keywords = "Analytical estimates, Analytical forms, Dominant contributions, 
                         In-Degree, nocv1, Random Walk, Static model, Time dependent, 
                         Watts-strogatz models.",
             abstract = "In this work, we propose a scheme that provides an analytical 
                         estimate for the time-dependent degree distribution of some 
                         networks. This scheme maps the problem into a random walk in 
                         degree space, and then we choose the paths that are responsible 
                         for the dominant contributions. The method is illustrated on the 
                         dynamical versions of the Erdos-R{\'e}nyi and Watts-Strogatz 
                         graphs, which were introduced as static models in the original 
                         formulation. We have succeeded in obtaining an analytical form for 
                         the dynamics Watts-Strogatz model, which is asymptotically exact 
                         for some regimes.",
                  doi = "10.1103/PhysRevE.95.012321",
                  url = "http://dx.doi.org/10.1103/PhysRevE.95.012321",
                 issn = "1539-3755",
             language = "en",
           targetfile = "casagrande_random.pdf",
        urlaccessdate = "23 nov. 2020"
}


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