Relevance of Complex Network Properties Philippe Giabbanelli «Impact of complex network properties on routing in backbone networks» Philippe Giabbanelli, CCNet 2010 (IEEE Globecom)

P. GiabbanelliRelevance of complex network properties1 Outline What can we measure in a network? Finding out what’s useful to measure You know how good something could be: build it! Related work on measures

P. GiabbanelliRelevance of complex network properties2 What can we measure in a network? Example #1: Social networks Property: average distance Measure: distance

P. GiabbanelliRelevance of complex network properties3 What can we measure in a network? Example #2: Obesity map Measure: Centrality

P. GiabbanelliRelevance of complex network properties4 What can we measure in a network? Example #3: Backbone network

P. GiabbanelliRelevance of complex network properties5 What can we measure in a network? NetworkProcessMeasures Social network Disease spread Factors incluencing obesity Obesity level Backbone networkDeploying equipment Average distance Centrality ???

P. GiabbanelliRelevance of complex network properties6 Finding out what’s useful to measure 1 – Modelling the main features ▪ Planar network ▪ There is a request between all pairs ◦ bandwidth from lognormal dist. ▪ Each edge is supported by several ports, all offering same bandwidth ▪ Goal: minimize total number of ports ($$$)

P. GiabbanelliRelevance of complex network properties7 Finding out what’s useful to measure 2 – Simulating ◦ Use a random planar graph generator (released in 2010) ◦ Create requests using probability: ◦ Optimize the number of ports to install ◦ Use several measures on the network and record the optimal number of ports

P. GiabbanelliRelevance of complex network properties8 Finding out what’s useful to measure 3 – Analysis ◦ We recorded several measures. Which ones best indicate the # of ports? ◦ Using data mining, we built classifiers and looked at their accuracy. < 9% error

P. GiabbanelliRelevance of complex network properties9 Finding out what’s useful to measure 3 – Analysis ◦ Routers are often of the same kind: same # ports. ◦ What happens if we also want to balance the charge? ◦ Same measures, and still ≈10% prediction error.

P. GiabbanelliRelevance of complex network properties10 From analysis to building ◦ We identified key measures to get efficient networks wrt ports. ◦ Now let’s build networks that score well on such measures. ◦ Networks must be incremental: add nodes with capacity needs. ◦ Space-filling networks were the best ones.

P. GiabbanelliRelevance of complex network properties11 Perspectives ◦ Traffic changes over time. ◦ When deploying a network, capacity is 100% over peak… ◦ …but what about managing? ◦ Turn ports off to save energy ◦ Green networks: hot topic.

P. GiabbanelliRelevance of complex network properties12 Related work on measures ◦ Knowing which measures are relevant to analyze a problem isn’t the end ◦ Computing measures for large networks (often happen) can be very long « Computing the average path length and a label-based routing in a small- world graph », P. Giabbanelli, D. Mazauric, S. Pérennes, AlgoTel 2010 « On the average path length of deterministic and stochastic networks », P. Giabbanelli, D. Mazauric, J.-C. Bermond, CompleNet 2010 ◦ Collaborated on theorems for average distance in a class of networks: ◦ Extended the work by considering a network with probabilistic growth:

P. GiabbanelliRelevance of complex network properties13 Related work on measures

P. GiabbanelliRelevance of complex network properties14 Questions ?!