Multidimensional Analysis of Complex Networks
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Multidimensional Analysis of Complex Networks

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A new study of how complex networks evolve along the two most important informative axes, space and time.

A new study of how complex networks evolve along the two most important informative axes, space and time.

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Multidimensional Analysis of Complex Networks Multidimensional Analysis of Complex Networks Presentation Transcript

  • Motivation Multidimensional Spatial analysis Growth analysis Multidimensional analysis of complex networks Possamai Lino Alma Mater Studiorum Università di Bologna Università di Padova Ph.D. Dissertation Defense February 21st, 2013Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 1/39
  • Motivation Multidimensional Spatial analysis Growth analysisPublications and conferences list Plos One 2012 Thi Hoang, Sun, Possamai, JafariAsbagh, Patil, Menczer Scholarometer: A Social Framework for Analyzing Impact across Disciplines IPM 2012 Sun, Kaur, Possamai, Menczer Ambiguous Author Query Detection using Crowdsourced Digital Library Annotations SocialCom11 2011 Sun, Kaur, Possamai and Menczer Detecting 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 in Multiple Myeloma Sunbelt2010 2010 Marchiori, Possamai Telescopic analysis of complex networks PRIB2009 2009 Forcato, Possamai, Ferrari, Agnelli, Todoerti, Lambertenghi, Bortoluzzi, Marchiori et al. Reverse Engineering and Critical Analysis of Gene Regulatory Networks in Multiple Myeloma (under submission) 2013 Toward an optimized evolution of social networks (under submission) 2013 Micro-macro analysis of complex networksPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 2/39
  • Motivation Multidimensional Spatial analysis Growth analysisOutline 1 Motivation 2 Multidimensional Introduction 3 Spatial analysis Introduction Algorithm Datasets Results 4 Growth analysis Motivation Growth dynamics Simulations ResultsPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 3/39
  • Motivation Multidimensional Spatial analysis Growth analysisDomain A complex system is a network of elements that interacts in a non-linearly way, resulting in an overall behavior that is difficult to predict.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 4/39
  • Motivation Multidimensional Spatial analysis Growth analysisDomain A complex system is a network of elements that interacts in a non-linearly way, resulting in an overall behavior that is difficult to predict. The digitalization of every day’s actions allows a deeper investigation on how persons, computers, animals, companies etc interactPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 4/39
  • Motivation Multidimensional Spatial analysis Growth analysisDomain A complex system is a network of elements that interacts in a non-linearly way, resulting in an overall behavior that is difficult to predict. The digitalization of every day’s actions allows a deeper investigation on how persons, computers, animals, companies etc interact Networks are everywhere in Nature: from ecology to the WWW, to food chain, to social networks, to financePossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 4/39
  • Motivation Multidimensional Spatial analysis Growth analysisDomain A complex system is a network of elements that interacts in a non-linearly way, resulting in an overall behavior that is difficult to predict. The digitalization of every day’s actions allows a deeper investigation on how persons, computers, animals, companies etc interact Networks are everywhere in Nature: from ecology to the WWW, to food chain, to social networks, to finance This opened up many interdisciplinary research areas that are very activePossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 4/39
  • Motivation Multidimensional Spatial analysis Growth analysisHistory ˝ 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 power law in the degree distribution Many other works that followed, proposed improvements in the basic statistics and in the generative modelsPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 5/39
  • Motivation Multidimensional Spatial analysis Growth analysisMotivation The aim of this Thesis was to study Complex Networks (CN) under the most important dimensions. Key points are the following: Currently, many studies on CN underestimate the effect of spatial constraints on the overall evolution Many models have been proposed in order to create CNs with the same properties of the observed networks However, they are not sufficient to describe precisely how networks evolve That is why other instincts might be at the root of the growth No 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 lacking features. We call it multidimensional.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 6/39
  • Motivation Multidimensional Spatial analysis Growth analysisIntroduction So what do we mean by multidimensional? We mean a novel framework that analyzes complex networks (CN) along the two fundamental informative axes:Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 7/39
  • Motivation Multidimensional Spatial analysis Growth analysisIntroduction So what do we mean by multidimensional? We mean a novel framework that analyzes complex networks (CN) along the two fundamental informative axes: SpacePossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 7/39
  • Motivation Multidimensional Spatial analysis Growth analysisIntroduction So what do we mean by multidimensional? We mean a novel framework that analyzes complex networks (CN) along the two fundamental informative axes: Space Time The study of these dimensions was performed by freezing one axis and simulating the evolution of the otherPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 7/39
  • Motivation Multidimensional Spatial analysis Growth analysisIntroduction T HE SPACE DIMENSIONPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 8/39
  • Motivation Multidimensional Spatial analysis Growth analysisIntroductionSpace dimension The structure of a CN is not 100% completely defined because it depends on the level of detail with which the system is observed For instance, biological networks could be analyzed at different layers. 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 the detail levels. Results, properties, features that are valid in a specific level might not hold in other levels.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 9/39
  • Motivation Multidimensional Spatial analysis Growth analysisAlgorithmSpatial Analysis So what does it means to view a network at a particular level? Let us take a spatial network with information about nodes’ positions over a plane.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 10/39
  • Motivation Multidimensional Spatial analysis Growth analysisAlgorithmSpatial Analysis So what does it means to view a network at a particular level? Let us take a spatial network with information about nodes’ positions over a plane. Viewing a network at different precision levels corresponds to viewing the network at a difference distance from a point of view.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 10/39
  • Motivation Multidimensional Spatial analysis Growth analysisAlgorithmSpatial Analysis So what does it means to view a network at a particular level? Let us take a spatial network with information about nodes’ positions over a plane. Viewing a network at different precision levels corresponds to viewing the network at a difference distance from a point of view. This process is modeled utilizing a concept that comes from the human eyes ability to distinguish two points at some distance from the observer. The points are nodes of the network with x, y coordinates over a plane.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 10/39
  • Motivation Multidimensional Spatial analysis Growth analysisAlgorithmSpatial Analysis Generally, the telescopic algorithm is a function t : (G × f ) → G′ that takes as input: a graph G fuzziness f (distance) and produces a resulting graph G′Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 11/39
  • Motivation Multidimensional Spatial analysis Growth analysisAlgorithmSpatial Analysis Generally, the telescopic algorithm is a function t : (G × f ) → G′ that takes as input: a graph G fuzziness f (distance) and produces a resulting graph G′ In order to emulate the network abstraction capability, we placed a virtual grid on top of the input graph. Cell’s dimensions depend on the fuzziness value.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 11/39
  • Motivation Multidimensional Spatial analysis Growth analysisAlgorithmSpatial Analysis All the nodes belonging to the same cell are collapsed and represented by a unique node in the new graph. If there is an edge from at least one node of the i cell to at least one of the j cell then the (i, j) edge exists in the new graph G′ . With these rules, the long range edges are preserved.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 12/39
  • Motivation Multidimensional Spatial analysis Growth analysisAlgorithmSpatial Analysis By repeatedly applying this function we create a fuzziness-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 telescopic spectrum of a network, and study, wrt each property of interest, what changes in the micro-macro shift (in [Sunbelt2010]).Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 13/39
  • Motivation Multidimensional Spatial analysis Growth analysisDatasetsTracking properties To characterize the structural properties during the abstraction process, we consider 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: t 1 1 m 1 1 Eglob = Eglob = n(n − 1) i=j hij n(n − 1) i=j δij Topological and metrical local efficiency Topological and metrical costs: |E| i=j aij lij Ct = Cm = n(n − 1)/2 i=j lij Homophily (degree correlation)Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 14/39
  • Motivation Multidimensional Spatial analysis Growth analysisDatasetsNetwork datasets Two different classes of networks are considered:Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 15/39
  • Motivation Multidimensional Spatial analysis Growth analysisDatasetsNetwork datasets Two different classes of networks are considered: Four subway networks are considered: two from the U.S., Boston and New York and two from Europe, Paris and MilanPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 15/39
  • Motivation Multidimensional Spatial analysis Growth analysisDatasetsNetwork datasets Two different classes of networks are considered: Four subway networks are considered: two from the U.S., Boston and New York and two from Europe, Paris and Milan The US airline networkPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 15/39
  • Motivation Multidimensional Spatial analysis Growth analysisDatasetsNetwork datasets Two different classes of networks are considered: Four subway networks are considered: two from the U.S., Boston and New York and two from Europe, Paris and Milan The US airline network The VirtualTourist online social network (*) They all are undirected networks.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 15/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsGlobal Efficiency 1 1 Topological Eglob 0.8 0.8 Metrical Eglob 0.6 0.6 0.4 Bos 0.4 Bos NYC NYC 0.2 Par 0.2 Par Mil Mil 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fuzziness Fuzziness We found different results by considering topological and metrical efficiency Topological: networks with high efficiency at macro level might have low Eglob at micro Metrical: stable under detail levels variation.Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 16/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsGlobal Efficiency 1 1 Topological Eglob 0.8 0.8 Metrical Eglob 0.6 IT 0.6 IT UK UK 0.4 NL 0.4 NL AU AU 0.2 IN 0.2 IN Air Air 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fuzziness Fuzziness All the curves start at higher values because of the better structure of SM-SF networks Both subways and SM-SF networks will be simpler as f increases, more efficient, but indistinguishablePossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 17/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsLocal Efficiency 1 1 Bos Bos Topological Eloc 0.8 Par 0.8 Par Metrical Eloc Mil Mil 0.6 NYC 0.6 NYC 0.4 0.4 0.2 0.2 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fuzziness Fuzziness 1 1 IT Topological Eloc 0.8 0.8 UK Metrical Eloc NL 0.6 IT 0.6 AU UK IN 0.4 NL 0.4 Air AU 0.2 IN 0.2 Air 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fuzziness Fuzziness Eloc is stable under our telescopic framework. Low values of local clustering maintained throughout the spectrum Results strongly differ from subways. This clearly means that the abstraction process is able to distinguish the two different principles that guided the evolutionPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 18/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsCost 1 1 Bos Bos 0.8 NYC 0.8 NYC Par Par 0.6 Mil 0.6 Mil Cm Ct 0.4 0.4 0.2 0.2 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fuzziness Fuzziness It might be counterintuitive that simple (abstracted) networks are expensive The cost is directly connected to the efficiency of a networkPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 19/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsCost 1 1 0.8 0.8 0.6 IT 0.6 IT Cm Ct UK UK 0.4 NL 0.4 NL AU AU 0.2 IN 0.2 IN Air Air 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fuzziness Fuzziness However, when compared to SM-SF networks turn out that the inborn economic principles that characterize subways are maintainedPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 20/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsRandomized fuzziness-varying graphs In order to understand how the topological and metrical structure of CNs is affected by the spatial analysis, we used also null models in our simulationsPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 21/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsRandomized fuzziness-varying graphs In order to understand how the topological and metrical structure of CNs is affected by the spatial analysis, we used also null models in our simulations In 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 PadovaMultidimensional analysis of complex networks 21/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsEvolution on randomized networks 1 1 Boston Boston Topological Eglob 0.8 0.8 Metrical Eglob 0.6 0.6 Norm Norm 0.4 +r 0.4 +r +a +a 0.2 +n 0.2 +n +s +s 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fuzziness Fuzziness t In Eglob , 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 PadovaMultidimensional analysis of complex networks 22/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsEvolution on randomized networks 1 1 Aus Aus Topological Eglob 0.8 0.8 Metrical Eglob 0.6 0.6 Norm Norm 0.4 +r 0.4 +r +a +a 0.2 +n 0.2 +n +s +s 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fuzziness Fuzziness Random perturbations do not alter Eglob because random networks are by definition very efficient The destroying effect found in subways is also present but constrained to small values of f in metrical efficiency SM-SF are robust because the randomizations do not alter considerably the networks on the spectrumPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 23/39
  • Motivation Multidimensional Spatial analysis Growth analysisMotivation T HE TIME DIMENSIONPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 24/39
  • Motivation Multidimensional Spatial analysis Growth analysisMotivationTime analysis Many researches in the literature have dealt with proposing generative models that uncover the key ingredients of network evolution These are based on simple and advanced local rules that produce a global behavior that is similar to the steady-state target’s network Since many of them are based on social systems, we also concentrate on these types of CNsPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 25/39
  • Motivation Multidimensional Spatial analysis Growth analysisGrowth dynamicsGrowth rule IThe random rule assumes that:DefinitionNodes of the networks randomly connect each other withuniform probability pij = kEmpirical tests discovered that real world networks are far frombeing randomPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 26/39
  • Motivation Multidimensional Spatial analysis Growth analysisGrowth dynamicsGrowth rule IIThe rule of Preferential attachment assumes that:DefinitionOlder nodes are more likely to acquire new linkscompared to new ones. ki Π(ki ) = j kjPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 27/39
  • Motivation Multidimensional Spatial analysis Growth analysisGrowth dynamicsGrowth rule IIIThe Social rule assumes that:Definitionif 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 in many networks) Clearly, these rules are not sufficient to completely describe the evolution of social networks. There must be some other instincts that trigger the network evolutionPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 28/39
  • Motivation Multidimensional Spatial analysis Growth analysisGrowth dynamicsSettings with special nodes The contribution of this Thesis is to understand whether new instincts on top of the previous growth models can leverage the users’ commitment in networks Insight on network evolution with special nodesPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 29/39
  • Motivation Multidimensional Spatial analysis Growth analysisGrowth dynamicsSettings with special nodes The contribution of this Thesis is to understand mad whether new instincts on top of the previous growth models can leverage the users’ commitment in networks Insight on network evolution with special nodes m = number of sirens (6,12) a = attractiveness d = activation time spanPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 29/39
  • Motivation Multidimensional Spatial analysis Growth analysisGrowth dynamicsSettings with special nodes The contribution of this Thesis is to understand mad whether new instincts on top of the previous growth models can leverage the users’ commitment in networks 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 · dPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 29/39
  • Motivation Multidimensional Spatial analysis Growth analysisSimulationsSimulations Both sequential and simultaneous simulations are considered The network evolves according to one of the following rules random, aristocratic or social both at the users and sirens levels The entire system dynamics is accounted by two almost independent user and siren subprocesses that evolve according to the previous local rules In both cases, the future evolution Gt+1 will depend on GtPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 30/39
  • Motivation Multidimensional Spatial analysis Growth analysisSimulationsSimulations 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 q(s) a(s) = q(u) = 10 ∀u ∈ V s q(u) = 1 ∀u ∈ V u∈V ∪V s q(u) In simultaneous simulations, many edges can be created and this number varies as a function of Eglob E(Gt−1 ) et = 1 + C · · (nart−1 − 1) E(Gideal )Possamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 31/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsResults and Datasets At this point, based on the framework we provided, we are now able to answer the following 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 PadovaMultidimensional analysis of complex networks 32/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsResults and Datasets At this point, based on the framework we provided, we are now able to answer the following 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 PadovaMultidimensional analysis of complex networks 32/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsResults and Datasets At this point, based on the framework we provided, we are now able to answer the following 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 PadovaMultidimensional analysis of complex networks 32/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsResults and Datasets At this point, based on the framework we provided, we are now able to answer the following 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 and CommunitiesPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 32/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsQ1: Effectiveness In order to understand whether sirens are effective we compare the simulations with and without sirens 0.25 0.25 rnd rnd ari ari 0.2 soc 0.2 soc 0.15 0.15 Eglob Eglob 0.1 0.1 0.05 CM 0.05 CM + Sir 0 0 0 600 1200 1800 2400 3000 0 20 40 60 80 100 120 140 Step StepPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 33/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsQ2: 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 that perform best Results are valid for all the rules and networks considered 0.25 aristocratic 0.25 aristocratic Cs = 1200 Cs = 2400 0.2 0.2 0.15 0.15 Eglob Eglob 0.1 0.1 0.05 (12,10,10) 0.05 (12,10,20) (6,10,20) (12,20,10) (6,20,10) (6,20,20) 0 0 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 Step StepPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 34/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsQ3: Benefit We set the number of sirens and see how the other configuration parameters influence the growth behavior We clearly see that the benefit increases, as the cost gets higher. In fact, it is not proportional to Cs . 0.25 aristocratic 4000 rnd pref ari pref 0.2 CM+Sir 3000 soc pref 0.15 Eglob Cs 2000 0.1 (6,10,10) 1000 0.05 (6,10,20) (6,20,10) (6,20,20) 0 0 40 60 80 100 120 140 0 40 80 120 160 200 Tmin StepPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 35/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsRecap of contributions We introduced a new framework in which we consider the two most important informative axes along with a CN evolvesPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 36/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsRecap of contributions We introduced a new framework in which we consider the two most important informative axes along with a CN evolves The first, spatial analysis, deals with analyzing a network under different detail levels Subway networks indexes tend to be more stable under the telescopic variations Network properties change in the telescopic spectrum: their micro and macro behavior are differentPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 36/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsRecap of contributions We introduced a new framework in which we consider the two most important informative axes along with a CN evolves The first, spatial analysis, deals with analyzing a network under different detail levels Subway networks indexes tend to be more stable under the telescopic variations Network properties change in the telescopic spectrum: their micro and macro behavior are different The second, time analysis, models the growth of social networks by using a set of privileged nodes that promote network evolution These special nodes are an effective way to increase network efficiency The benefit increases as cost increases, however it is not proportional Invest on attractivenessPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 36/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsReferees reports From leading expert in the Complex System area Jesús Gómez Gardeñes (University of Zaragoza) Overall positive feedback Acknowledged contributions to state-of-the-artPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 37/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsClosing remarks and ongoing activities Consider more spatial networks in order to have a broader coverage and test whether our findings are still valid Study force-based network permutations such as Kamada-Kawai and Fruchterman-ReingoldPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 38/39
  • Motivation Multidimensional Spatial analysis Growth analysisResultsClosing remarks and ongoing activities Consider more spatial networks in order to have a broader coverage and test whether our findings are still valid Study force-based network permutations such as Kamada-Kawai and Fruchterman-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 the idea of “duplex” networked systems can be extended to digital librariesPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 38/39
  • Motivation Multidimensional Spatial analysis Growth analysisResults Thank youPossamai Lino Università di Bologna - Università di PadovaMultidimensional analysis of complex networks 39/39