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Motivation Multidimensional Spatial analysis Growth analysis
Multidimensional analysis of complex networks
Possamai Lino
Alma Mater Studiorum Università di BolognaUniversità di Padova
Ph.D. Dissertation DefenseFebruary 21st, 2013
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 1/39
Motivation Multidimensional Spatial analysis Growth analysis
Publications and conferences list
Plos One 2012 Thi Hoang, Sun, Possamai, JafariAsbagh, Patil, MenczerScholarometer: A Social Framework for Analyzing Impact across Disciplines
IPM 2012 Sun, Kaur, Possamai, MenczerAmbiguous Author Query Detection using Crowdsourced Digital Library Annotations
SocialCom11 2011 Sun, Kaur, Possamai and MenczerDetecting Ambiguous Author Names in Crowdsourced Scholarly Data
PSB2010 2010 Biasiolo, Forcato, Possamai, Ferrari, Agnelli, Lionetti, Todoerti, Neri, Marchiori et al.Critical analysis of transcriptional and post-transcriptional regulatory networks inMultiple Myeloma
Sunbelt2010 2010 Marchiori, PossamaiTelescopic analysis of complex networks
PRIB2009 2009 Forcato, Possamai, Ferrari, Agnelli, Todoerti, Lambertenghi, Bortoluzzi, Marchiori et al.Reverse Engineering and Critical Analysis of Gene Regulatory Networksin Multiple Myeloma
(under submission) 2013 Toward an optimized evolution of social networks
(under submission) 2013 Micro-macro analysis of complex networks
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 2/39
Motivation Multidimensional Spatial analysis Growth analysis
Outline
1 Motivation
2 MultidimensionalIntroduction
3 Spatial analysisIntroductionAlgorithmDatasetsResults
4 Growth analysisMotivationGrowth dynamicsSimulationsResults
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 3/39
Motivation Multidimensional Spatial analysis Growth analysis
Domain
A complex system is a network of elements thatinteracts in a non-linearly way, resulting in anoverall behavior that is difficult to predict.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 4/39
Motivation Multidimensional Spatial analysis Growth analysis
Domain
A complex system is a network of elements thatinteracts in a non-linearly way, resulting in anoverall behavior that is difficult to predict.
The digitalization of every day’s actions allows adeeper investigation on how persons, computers,animals, companies etc interact
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 4/39
Motivation Multidimensional Spatial analysis Growth analysis
Domain
A complex system is a network of elements thatinteracts in a non-linearly way, resulting in anoverall behavior that is difficult to predict.
The digitalization of every day’s actions allows adeeper investigation on how persons, computers,animals, companies etc interact
Networks are everywhere in Nature: from ecologyto the WWW, to food chain, to social networks, tofinance
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 4/39
Motivation Multidimensional Spatial analysis Growth analysis
Domain
A complex system is a network of elements thatinteracts in a non-linearly way, resulting in anoverall behavior that is difficult to predict.
The digitalization of every day’s actions allows adeeper investigation on how persons, computers,animals, companies etc interact
Networks are everywhere in Nature: from ecologyto the WWW, to food chain, to social networks, tofinance
This opened up many interdisciplinary researchareas that are very active
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 4/39
Motivation Multidimensional Spatial analysis Growth analysis
History
Started with mathematicians Erdos–Rényi and graph theory
Watts and Strogatz, small world and 〈L〉, C metrics
Barabási-Albert first introduced the scale-free model, identified hubs and powerlaw in the degree distribution
Many other works that followed, proposed improvements in the basic statistics andin the generative models
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 5/39
Motivation Multidimensional Spatial analysis Growth analysis
Motivation
The aim of this Thesis was to study Complex Networks (CN) under the most importantdimensions. Key points are the following:
Currently, many studies on CN underestimate the effect of spatial constraints onthe overall evolutionMany models have been proposed in order to create CNs with the sameproperties of the observed networks
However, they are not sufficient to describe precisely how networks evolveThat is why other instincts might be at the root of the growthNo methods have been proposed to increase the commitment in users’ communities
For these reasons, we worked on a new framework that is based on these lackingfeatures. We call it multidimensional.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 6/39
Motivation Multidimensional Spatial analysis Growth analysis
Introduction
So what do we mean by multidimensional?
We mean a novel framework that analyzes complexnetworks (CN) along the two fundamentalinformative axes:
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 7/39
Motivation Multidimensional Spatial analysis Growth analysis
Introduction
So what do we mean by multidimensional?
We mean a novel framework that analyzes complexnetworks (CN) along the two fundamentalinformative axes:
Space
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 7/39
Motivation Multidimensional Spatial analysis Growth analysis
Introduction
So what do we mean by multidimensional?
We mean a novel framework that analyzes complexnetworks (CN) along the two fundamentalinformative axes:
Space
Time
The study of these dimensions was performed byfreezing one axis and simulating the evolution ofthe other
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 7/39
Motivation Multidimensional Spatial analysis Growth analysis
Introduction
THE SPACE DIMENSION
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 8/39
Motivation Multidimensional Spatial analysis Growth analysis
Introduction
Space dimension
The structure of a CN is not 100% completely defined because itdepends on the level of detail with which the system is observed
For instance, biological networks could be analyzed at differentlayers. Nodes could be represented as atoms, proteins, cells,neurons and so on
Until now, no one has considered to study CN as a function of thedetail levels.
Results, properties, features that are valid in a specific level mightnot hold in other levels.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 9/39
Motivation Multidimensional Spatial analysis Growth analysis
Algorithm
Spatial Analysis
So what does it means to view a network at a particularlevel?
Let us take a spatial network with information about nodes’positions over a plane.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 10/39
Motivation Multidimensional Spatial analysis Growth analysis
Algorithm
Spatial Analysis
So what does it means to view a network at a particularlevel?
Let us take a spatial network with information about nodes’positions over a plane.
Viewing a network at different precision levels correspondsto viewing the network at a difference distance from a pointof view.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 10/39
Motivation Multidimensional Spatial analysis Growth analysis
Algorithm
Spatial Analysis
So what does it means to view a network at a particularlevel?
Let us take a spatial network with information about nodes’positions over a plane.
Viewing a network at different precision levels correspondsto viewing the network at a difference distance from a pointof view.
This process is modeled utilizing a concept that comesfrom the human eyes ability to distinguish two points atsome distance from the observer.
The points are nodes of the network with x , y coordinatesover a plane.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 10/39
Motivation Multidimensional Spatial analysis Growth analysis
Algorithm
Spatial Analysis
Generally, the telescopic algorithm is a function t : (G × f ) → G′ that takes asinput:
a graph Gfuzziness f (distance)and produces a resulting graph G′
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 11/39
Motivation Multidimensional Spatial analysis Growth analysis
Algorithm
Spatial Analysis
Generally, the telescopic algorithm is a function t : (G × f ) → G′ that takes asinput:
a graph Gfuzziness f (distance)and produces a resulting graph G′
In order to emulate the network abstraction capability, we placed a virtual grid ontop of the input graph.
Cell’s dimensions depend on the fuzziness value.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 11/39
Motivation Multidimensional Spatial analysis Growth analysis
Algorithm
Spatial Analysis
All the nodes belonging to the same cell are collapsed andrepresented by a unique node in the new graph.
If there is an edge from at least one node of the i cell to atleast one of the j cell then the (i , j) edge exists in the newgraph G′.
With these rules, the long range edges are preserved.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 12/39
Motivation Multidimensional Spatial analysis Growth analysis
Algorithm
Spatial Analysis
By repeatedly applying this function we create afuzziness-varying family of graphs T = {G0,G1, . . .Gp}where p is the number of precision levels.
G0 is the micro view and Gp is the macro view.
This novel analysis then allows creating the telescopicspectrum of a network, and study, wrt each property ofinterest, what changes in the micro-macro shift (in[Sunbelt2010]).
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 13/39
Motivation Multidimensional Spatial analysis Growth analysis
Datasets
Tracking properties
To characterize the structural properties during the abstraction process, weconsider several features widely used in network literature
Number of nodes, edges, kmax , kmean, standard deviation of k
Physical, topological and metrical diameter
Topological and metrical efficiency:
E tglob =
1
n(n − 1)
∑
i 6=j
1
hijEm
glob =1
n(n − 1)
∑
i 6=j
1
δij
Topological and metrical local efficiency
Topological and metrical costs:
Ct =|E|
n(n − 1)/2Cm =
∑
i 6=j aij lij∑
i 6=j lij
Homophily (degree correlation)
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 14/39
Motivation Multidimensional Spatial analysis Growth analysis
Datasets
Network datasets
Two different classes of networks are considered:
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 15/39
Motivation Multidimensional Spatial analysis Growth analysis
Datasets
Network datasets
Two different classes of networks are considered:
Four subway networks are considered: two fromthe U.S., Boston and New York and two fromEurope, Paris and Milan
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 15/39
Motivation Multidimensional Spatial analysis Growth analysis
Datasets
Network datasets
Two different classes of networks are considered:
Four subway networks are considered: two fromthe U.S., Boston and New York and two fromEurope, Paris and Milan
The US airline network
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 15/39
Motivation Multidimensional Spatial analysis Growth analysis
Datasets
Network datasets
Two different classes of networks are considered:
Four subway networks are considered: two fromthe U.S., Boston and New York and two fromEurope, Paris and Milan
The US airline network
The VirtualTourist online social network (*)
They all are undirected networks.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 15/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Global Efficiency
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Top
olog
ical
Egl
ob
Fuzziness
BosNYCParMil
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Met
rical
Egl
ob
Fuzziness
BosNYCParMil
We found different results by considering topological and metrical efficiency
Topological: networks with high efficiency at macro level might have low Eglob atmicro
Metrical: stable under detail levels variation.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 16/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Global Efficiency
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Top
olog
ical
Egl
ob
Fuzziness
ITUKNLAUINAir
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Met
rical
Egl
ob
Fuzziness
ITUKNLAUINAir
All the curves start at higher values because of the better structure of SM-SFnetworks
Both subways and SM-SF networks will be simpler as f increases, more efficient,but indistinguishable
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 17/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Local Efficiency
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Top
olog
ical
Elo
c
Fuzziness
BosParMil
NYC
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Top
olog
ical
Elo
c
Fuzziness
ITUKNLAUINAir
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Met
rical
Elo
c
Fuzziness
BosParMil
NYC
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Met
rical
Elo
c
Fuzziness
ITUKNLAUINAir
Eloc is stable under our telescopic framework. Low values of local clusteringmaintained throughout the spectrumResults strongly differ from subways. This clearly means that the abstractionprocess is able to distinguish the two different principles that guided the evolution
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 18/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Cost
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Ct
Fuzziness
BosNYCParMil
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Cm
Fuzziness
BosNYCParMil
It might be counterintuitive that simple (abstracted) networks are expensive
The cost is directly connected to the efficiency of a network
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 19/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Cost
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Ct
Fuzziness
ITUKNLAUINAir
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Cm
Fuzziness
ITUKNLAUINAir
However, when compared to SM-SF networks turn out that the inborn economicprinciples that characterize subways are maintained
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 20/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Randomized fuzziness-varying graphs
In order to understand how the topological and metrical structure of CNs isaffected by the spatial analysis, we used also null models in our simulations
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 21/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Randomized fuzziness-varying graphs
In order to understand how the topological and metrical structure of CNs isaffected by the spatial analysis, we used also null models in our simulationsIn particular, we provided four models that account for different perturbations
+n, shuffling nodes’ positions+a, rewiring edges+r, that is the union of +n and +a+s, scale-free structure (using BA model)
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 21/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Evolution on randomized networks
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Top
olog
ical
Egl
ob
Fuzziness
BostonBoston
Norm+r+a+n+s
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Met
rical
Egl
ob
Fuzziness
Boston
Norm+r+a+n+s
In E tglob, randomizations increase the efficiency because they create the right
shortcuts that drop L
Conversely, randomness in a spatial context destroys the global efficiency. Indeed,when f > 0.3 all the networks will be indistinguishable.
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 22/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Evolution on randomized networks
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Top
olog
ical
Egl
ob
Fuzziness
Aus
Norm+r+a+n+s
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Met
rical
Egl
ob
Fuzziness
Aus
Norm+r+a+n+s
Random perturbations do not alter Eglob because random networks are bydefinition very efficient
The destroying effect found in subways is also present but constrained to smallvalues of f in metrical efficiency
SM-SF are robust because the randomizations do not alter considerably thenetworks on the spectrum
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 23/39
Motivation Multidimensional Spatial analysis Growth analysis
Motivation
THE TIME DIMENSION
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 24/39
Motivation Multidimensional Spatial analysis Growth analysis
Motivation
Time analysis
Many researches in the literature have dealt with proposing generative modelsthat uncover the key ingredients of network evolution
These are based on simple and advanced local rules that produce a globalbehavior that is similar to the steady-state target’s network
Since many of them are based on social systems, we also concentrate on thesetypes of CNs
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 25/39
Motivation Multidimensional Spatial analysis Growth analysis
Growth dynamics
Growth rule I
The random rule assumes that:
Definition
Nodes of the networks randomly connect each other withuniform probability
pij = k
Empirical tests discovered that real world networks are far frombeing random
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 26/39
Motivation Multidimensional Spatial analysis Growth analysis
Growth dynamics
Growth rule II
The rule of Preferential attachment assumes that:
Definition
Older nodes are more likely to acquire new linkscompared to new ones.
Π(ki ) =ki
∑
j kj
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 27/39
Motivation Multidimensional Spatial analysis Growth analysis
Growth dynamics
Growth rule III
The Social rule assumes that:
Definition
if two people have a friend in common then there is an increasedlikelihood that they will become friend in the future
This rule is at the root of the local clustering property (found inmany networks)
Clearly, these rules are not sufficient to completely describe theevolution of social networks.
There must be some other instincts that trigger the networkevolution
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 28/39
Motivation Multidimensional Spatial analysis Growth analysis
Growth dynamics
Settings with special nodes
The contribution of this Thesis is to understandwhether new instincts on top of the previous growthmodels can leverage the users’ commitment innetworks
Insight on network evolution with special nodes
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 29/39
Motivation Multidimensional Spatial analysis Growth analysis
Growth dynamics
Settings with special nodes
The contribution of this Thesis is to understandwhether new instincts on top of the previous growthmodels can leverage the users’ commitment innetworks
Insight on network evolution with special nodes
m = number of sirens (6,12)
a = attractiveness
d = activation time span
m a d
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 29/39
Motivation Multidimensional Spatial analysis Growth analysis
Growth dynamics
Settings with special nodes
The contribution of this Thesis is to understandwhether new instincts on top of the previous growthmodels can leverage the users’ commitment innetworks
Insight on network evolution with special nodes
m = number of sirens (6,12)
a = attractiveness
d = activation time span
configurations ci = (m, a, d)
configurations cost Cs = m · a · d
m a d
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 29/39
Motivation Multidimensional Spatial analysis Growth analysis
Simulations
Simulations
Both sequential and simultaneous simulations are considered
The network evolves according to one of the following rules random, aristocratic orsocial both at the users and sirens levels
The entire system dynamics is accounted by two almost independent user andsiren subprocesses that evolve according to the previous local rules
In both cases, the future evolution Gt+1 will depend on Gt
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 30/39
Motivation Multidimensional Spatial analysis Growth analysis
Simulations
Simulations
Sirens are used for a limited time span (d) after that the system will evolve by itself
Sirens acquire new links constantly over time as
es = |V s| · |V | · a
a is the attractiveness of the sirens
a(s) =q(s)
∑
u∈V∪V s q(u)q(u) = 10 ∀u ∈ V s q(u) = 1 ∀u ∈ V
In simultaneous simulations, many edges can be created and this number variesas a function of Eglob
et = 1 +
⌊
C ·E(Gt−1)
E(Gideal)· (nart−1 − 1)
⌋
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 31/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Results and Datasets
At this point, based on the framework we provided, we are now able to answer thefollowing set of fundamental questions:
Are the sirens effective in leveraging users’ commitment in new on line social networks?
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 32/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Results and Datasets
At this point, based on the framework we provided, we are now able to answer thefollowing set of fundamental questions:
Are the sirens effective in leveraging users’ commitment in new on line social networks?What are the best parameters for the same cost configurations?
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 32/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Results and Datasets
At this point, based on the framework we provided, we are now able to answer thefollowing set of fundamental questions:
Are the sirens effective in leveraging users’ commitment in new on line social networks?What are the best parameters for the same cost configurations?Is the benefit of sirens proportional to the amount of money involved?
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 32/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Results and Datasets
At this point, based on the framework we provided, we are now able to answer thefollowing set of fundamental questions:
Are the sirens effective in leveraging users’ commitment in new on line social networks?What are the best parameters for the same cost configurations?Is the benefit of sirens proportional to the amount of money involved?
We were particularly interested in on line social networks like VirtualTourist andCommunities
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 32/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Q1: Effectiveness
In order to understand whether sirens are effective we compare the simulationswith and without sirens
0
0.05
0.1
0.15
0.2
0.25
0 600 1200 1800 2400 3000
Egl
ob
Step
CM
rndari
soc
0
0.05
0.1
0.15
0.2
0.25
0 20 40 60 80 100 120 140
Egl
ob
Step
CM + Sir
rndari
soc
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 33/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Q2: Best parameter
What are the best parameters in the siren configurations ci = (m, a, d)?
The configurations that have the higher value of attractiveness are the ones thatperform best
Results are valid for all the rules and networks considered
0
0.05
0.1
0.15
0.2
0.25
0 10 20 30 40 50 60 70 80
Egl
ob
Step
aristocraticCs = 1200
(12,10,10)(6,10,20)(6,20,10)
0
0.05
0.1
0.15
0.2
0.25
0 10 20 30 40 50 60 70
Egl
ob
Step
aristocraticCs = 2400
(12,10,20)(12,20,10)
(6,20,20)
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 34/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Q3: Benefit
We set the number of sirens and see how the other configuration parametersinfluence the growth behavior
We clearly see that the benefit increases, as the cost gets higher. In fact, it is notproportional to Cs.
0
0.05
0.1
0.15
0.2
0.25
0 40 80 120 160 200
Egl
ob
Step
aristocratic
CM+Sir
(6,10,10)(6,10,20)(6,20,10)(6,20,20) 0
1000
2000
3000
4000
40 60 80 100 120 140
Cs
Tmin
rnd prefari pref
soc pref
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 35/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Recap of contributions
We introduced a new framework in which we consider the two most importantinformative axes along with a CN evolves
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 36/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Recap of contributions
We introduced a new framework in which we consider the two most importantinformative axes along with a CN evolvesThe first, spatial analysis, deals with analyzing a network under different detaillevels
Subway networks indexes tend to be more stable under the telescopic variationsNetwork properties change in the telescopic spectrum: their micro and macro behaviorare different
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 36/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Recap of contributions
We introduced a new framework in which we consider the two most importantinformative axes along with a CN evolvesThe first, spatial analysis, deals with analyzing a network under different detaillevels
Subway networks indexes tend to be more stable under the telescopic variationsNetwork properties change in the telescopic spectrum: their micro and macro behaviorare different
The second, time analysis, models the growth of social networks by using a set ofprivileged nodes that promote network evolution
These special nodes are an effective way to increase network efficiencyThe benefit increases as cost increases, however it is not proportionalInvest on attractiveness
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 36/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Referees reports
From leading expert in the Complex System areaJesús Gómez Gardeñes (University of Zaragoza)
Overall positive feedbackAcknowledged contributions to state-of-the-art
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 37/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Closing remarks and ongoing activities
Consider more spatial networks in order to have a broader coverage and testwhether our findings are still valid
Study force-based network permutations such as Kamada-Kawai andFruchterman-Reingold
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 38/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Closing remarks and ongoing activities
Consider more spatial networks in order to have a broader coverage and testwhether our findings are still valid
Study force-based network permutations such as Kamada-Kawai andFruchterman-Reingold
Define network growth that consider mixed rules instead of independent ones
Study the evolution by simultaneously varying the two axes
Continue the work done at Indiana University and in particular verify whether theidea of “duplex” networked systems can be extended to digital libraries
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 38/39
Motivation Multidimensional Spatial analysis Growth analysis
Results
Thank you
Possamai Lino Università di Bologna - Università di Padova
Multidimensional analysis of complex networks 39/39