Time Evolution of the Importance of Nodes in dynamic Networks
Résumé
For a long time now, researchers have worked on
defining different metrics able to characterize the importance
of nodes in networks. Among them, centrality measures have
proved to be pertinent as they relate the position of a node in the
structure to its ability to diffuse an information efficiently. The
case of dynamic networks, in which nodes and links appear and
disappear over time, led the community to propose extensions of
those classical measures. Yet, they do not investigate the fact that
the network structure evolves and that node importance may
evolve accordingly. In the present paper, we propose temporal
extensions of notions of centrality, which take into account the
paths existing at any given time, in order to study the time
evolution of nodes' importance in dynamic networks. We apply
this to two datasets and show that the importance of nodes does
indeed vary greatly with time. We also show that in some cases it
might be meaningless to try to identify nodes that are consistently
important over time, thus strengthening the interest of temporal
extensions of centrality measures.
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