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SUMMARY:Dynamics\, Robustness and Multiscale Modularity of Complex Network
 s - Renaud Lambiotte\, Institute for Mathematical Sciences\, Imperial Coll
 ege London.
DTSTART:20091109T143000Z
DTEND:20091109T153000Z
UID:TALK21370@talks.cam.ac.uk
CONTACT:Neil Walton
DESCRIPTION:The complex structure of many social\, information and biologi
 cal\nnetworks is underpinned by communities at different scales. These\nto
 pological modules are often indicative of underlying features and\nfunctio
 nalities\, such as tightly-knit groups of metabolites or species\nin biolo
 gical networks. The presence of well-defined communities also\nhas an effe
 ct on the dynamics taking place on a network. A variety of\nmethods and me
 asures have been proposed to uncover these modules\, most\nnotably modular
 ity and spectral partitioning. However\, these\napproaches are based on st
 ructural\, static properties of the network.\nHere I introduce a definitio
 n for the quality of the partition of a\nnetwork that is based on the stat
 istical properties of a dynamical\nprocess taking place on the graph. This
  measure\, denoted the stability\nof the partition\, has an intrinsic depe
 ndence on the time-scale of the\nprocess\, which can be used to uncover co
 mmunity structures at\ndifferent resolutions. The stability extends and un
 ifies standard\ncommunity detection algorithms. In particular\, both modul
 arity and\nspectral partitioning are shown to have a dynamical interpretat
 ion in\nthe case of undirected networks and can be seen as limiting cases 
 of\nthe stability. In the case of directed networks\, however\, stability\
 ndiffers from modularity by its non-local nature as it is based on the\npe
 rsistence of probabilistic flows in modules. I conclude by\ndiscussing the
  optimisation of stability for large networks and the\npossibility to sele
 ct the most significant scales of description by\nmeasuring their robustne
 ss.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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