On the relevance of the edge-Markovian evolving graph model for real mobile networks

By

Aurélie Faure de Pebeyre, Fabien Tarissan et Julien Sopena

IFIP Wireless Days conference (WD'13), Valencia, Spain, 2013

Abstract

The development of wireless devices led the scientific community
to focus more and more on systems of interaction composed of
moving entities. In this context, different models have been
proposed in an attempt to capture properties of the observed
dynamics. Among those models, the edge-Markovian evolving graph
model is appealing since it enables to highlight temporal
dependencies in the evolution of the graphs. This model relies on
two parameters accounting respectively for the creation and
suppression of links in the graph. Thus it assumes that these two
parameters are sufficient to characterise the dynamics during all
the evolution of the graph. In this paper, we test this
hypothesis by confronting the model to 6 datasets recording real
traces of evolving networks. In particular, we study the
proportion of created and deleted links over the time. The
results show that 5 of the 6 case studies present an
heterogeneous distribution of those fractions which contradicts
the underlying hypothesis of the model. Besides, in order to
understand the importance this might have as regard structural
properties of real networks, we also study the impact the
Markovian model has on the mean degree over the time. It turns
out that even in the suitable case, the model fails to reproduce
correctly this property which indicates its inadequacy for even
more complex properties of real evolving networks

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