1. PhD Thesis Proposal Evolution in Social Networks Candidate Giulio Rossetti Supervisor Dino Pedreschi Supervisor Fosca Giannotti Pisa, Computer Science Dept. 19th December 2012

2. Presentation Outline I° State of the Art Network Science Multidimensionality Time and Evolution Open Problems Structural issues Topological issues Evolutive issues Proposal What I've done so far… … and what’s my roadmap

3. Network Science Networks are everywhere – Social interactions, transportation, technological (WWW), biological, economics… Study their structures is an interesting task for a wide set of fields – Computer Science, Physics, Sociology… Through the analysis of networks is possible the discovery (and understanding) of hidden phenomena otherwise difficult to describe – Graph Theory In this technological era, huge networked datasets are easy to collect – Online Social Networks (OSNs), co-authorship networks, product nteworks… State of the Art

4. How can we describe real world phenomena? Observation The analysis of real world phenomena unveil peculiar charateristic that can be used to describe various typology of networks. Problem Can we build models that generate synthetic networks accordingly? Proposed models – Random Graphs – Small World – Scale Free – Forest Fire State of the Art

5. Random Graphs & Small World Rarely natural phenomena can be described by regularly connected graphs (such as lattices) and, at the same time, they do not show complete randomness. – [1967] Stanley Milgram: Six degree of separation – [1998] Watts & Strogatz: Small World State of the Art

6. Scale Free & Forest Fire Scale Free Model [1999] Barabàsi-Albert: Preferential Attachment – “Richer nodes became richer” – Power Law degree distribution State of the Art Forest Fire model [2005] Leskovetc: Community Structure – Shrinking diameter – Power Law degree distribution

7. Multidimensionality Social Networks are often multidimensional: – Multiple relations could occour among a couple of nodes at the same time Study the interplay among dimensions provides useful informations – Dependence among dimensions, redondance, exclusivity State of the Art [2011] Berlingerio et. al: Foundations of multidimensional network analysis

8. New measures are needed State of the Art A new set of Neighbor functions Functions able to analyze dimensions and their relevance

9. Internetworking Scenario & Hub Analysis In this multidimensional setting Hubs needs to be redefined… – [2011] Berlingerio et al.: The pursuit of hubbines State of the Art Data from Online Social Networks could be merged in order to obtain “Social Internetworking Scenarios” (SISs)

10. Time and Evolution State of the Art Networks are not static objects – Nodes and edges appear and disappear over time – Interactions among the same two nodes could take place multiple times Even when the structure could be assumed frozen in time – Diffusion processes – Information spreading – …

11. Link Prediction & Information Propagation Link Prediction Identify the rising of new edges observing the actual topology of a network is a complex task – [2003] Kleinberg et al.: The link prediction problem for social networks – [2011] Wang et al.: Human mobility, social ties, and link prediction. State of the Art Information Propagation How rapidly actions became viral? Every action lead necessary to a cascading effect? – [2008] Ma et al.: Mining social networks using heat diffusion processes for marketing candidates selection – [2009] Berlingerio et al.: Mining the information propagation in a network

12. Presentation Outline II° State of the Art Network Science Multidimensionality Time and Evolution Open Problems Structural issues Topological issues Evolutive issues Proposal What I've done so far… … and what’s my roadmap

13. Open Problems StructuralTopologicalEvolutive Node & Link Analysis Ego-networks, Communities, … Link Prediction, Community Evolution, … Open Problems

14. Structural issues “The structure of a network define how the parts of it (nodes and edges) relate to each other, how it is assembled” Open Problems The first step needed to understand how a network evolve is to study how its basic components (nodes and edges) can be characterized – Link analysis – Node analysis

15. Multidimensional Tie strength & Node Ranking Tie Strength Not all the social connections have the same degree of intimacy – [1973] Granovetter: The strength of weak ties What is a “strong” tie in a multidimensional networks? – Can we exploit this information? Open Problems Node Ranking Can we rank nodes in a multidimensional social graph? – For a person is better to have higher “skills” or being well connected within the network?

16. Topological issues “Network Topology express the particular shape the nodes are arranged” Open Problems 1.Nodes and edges in a network are organized in complex topologies (i.e. ego- networks, communities…); 2.Since in real networks entities are (strictly) related to each other we need to take care of topology when we want to model their evolution. – Community Discovery – …

17. Community Discovery The aim of CD algorithms is to identify communities hidden into complex network structure Why Community Discovery? “Cluster” homogeneous nodes relying on topological information (Clustering networked entities) Issues: – Each algorithm model different properties of real world communities – Found an acceptable compromise between number of communities and their sizes Context Dependent – Multidimensonal communities? Open Problems

18. Evolutive issues “Evolution is the process of change in all forms of networks over generations, and evolutionary analysis is the study of how evolution occurs.” Open Problems 1.Networks are dynamic objects; 2.Structure and Topology changes as time goes by; 3.Novel problems arise: – Community Evolution – Link Prediction – …

19. Community Evolution & Link Prediction Community Evolution Social groups change over time, can we identify how? – Community Kernel – Community Life-Cicle – Identify nodes roles – … Open Problems Link Prediction Social connections arise\renovate\disappear over time, can we predict how? – Temporal Link Prediction – Network Archeology – Multidimensional Link Prediction – …

20. Presentation Outline III° State of the Art Network Science Multidimensionality Time and Evolution Open Problems Structural issues Topological issues Evolutive issues Proposal What I've done so far… … and what’s my roadmap

21. Thesis Proposal Title: Evolution in Social Networks Aim: Exploit structural and topological patterns in order to model and understand evolutionary behavior of social networks. Proposal Understandig properties of Network’s Structure Topological Analysis Evolution in Social Networks

22. What I've done so far… Evolutive Analysis Giulio Rossetti, Michele Berlingerio, Fosca Giannotti, “Scalable Link Prediction on Multidimensional Networks”, ICDM DaMNET 2011 IEEE Giulio Rossetti, Michele Berlingerio and Fosca Giannotti, “Link Prediction su Reti Multidimensionali”, SEBD 2011 Topological Analysis Michele Coscia, Giulio Rossetti, Fosca Giannotti, Dino Pedreschi “DEMON: a Local-First Discovery Method for Overlapping Communities”, KDD 2012 ACM SIGKDD Structural Analysis Giulio Rossetti, Luca Pappalardo, Dino Pedreschi “How well do we know each other?: Detecting tie strength in multidimensional social networks”, ASONAM CSNA 2012 IEEE Proposal

23. …and what’s my roadmap Evolutive Analysis Temporal Link Prediction Community Life- Cycle Diffusion of informations Trust\Privacy feedbacks … Topological Analysis Kernel Communities Roles of nodes within Communities Multidimensional Community Discovery … Structural Analysis Strength of complex structures (ego-networks, communities…) Multidimensional Multilabel Node Ranking …. Proposal

24. Conclusion Evolutionary analysis of social networks represent a set of interdisciplinary problems. Given the availability of Big Datasets this kind of studies are today feasible on reasonable samples of individuals Proposal

25. Essential Bibliography Proposal [1] S. Milgram. The small world problem. Psychol, pages 60–67, 1967 [2] M. S. Granovetter. The strength of weak ties. America Journal of Sociology, 1973. [3] D. J. Watts and S. H. Strogatz. Collective dynamics of ’small-world’ networks. Nature, 1998 [4] A. L. Barabasi and R. Albert. Emergence of scaling in random networks. In Science, 1999 [5] D. Liben-Nowell and J. Kleinberg. The link prediction problem for social networks. In CIKM, 2003 [6] J. Leskovec, J. M. Kleinberg, and C. Faloutsos. Graphs over time: densification laws, shrinking diameters and possible explanations. In KDD, 2005 [7] H. Ma, H. Yang, M. R. Lyu, and I. King. Mining social networks using heat diffusion processes for marketing candidates selection. In CIKM, 2008 [8] M. Berlingerio, M. Coscia, and F. Giannotti. Mining the information propagation in a network. In SEBD, 2009 [9] M. Berlingerio, M. Coscia, F. Giannotti, A. Monreale, and D. Pedreschi. Foundations of multidimensional network analysis. In ASONAM, 2011 [10] D. Wang, D. Pedreschi, C. Song, F. Giannotti, and A. L. Barabàsi. Human mobility, social ties, and link prediction. In KDD, 2011 [11] M. Coscia, G. Rossetti, D. Pedreschi and F. Giannotti. DEMON: a Loca-first discovery method for overlapping communities, In KDD, 2012

26. First year original results Appendix How well do we know each other? Detecting tie strength in multidimensional social networks DEMON a local-first approach to community discovery Scalable Link Predition on Multidimensional Networks

27. Multidimensional Tie Strength Appendix Problem: Given a SIS scenario, are we able to identify strong ties? What they represent? Proposed Metric: Connection Redundancy: Node Similarity and Interactions: Results:

28. Community Discovery Appendix Problem: Given a complex network are we able to identify meaningful communities form a social point of view? Proposed Algorithm(s): – DEMON – Hierarchical DEMON

29. Community Discovery (2) Appendix DEMON algorithm: For each node n: Extract the Ego Network of n Remove n from the Ego Network Perform a Label Propagation 1 Insert n in each community found Update the raw community set C For each raw community c in C Merge with “similar” ones in the set (given a threshold) (i.e. merge iff at most the ε% of the smaller one is not included in the bigger one)

30. Appendix Community Discovery (3) Hierarchical DEMON algorithm: HDemon(Graph G) Cc = connectedComponent(G) C = ExtractCommunities(G) while (|C|>Cc) For c in C: N <- N ∪ make_node(c) For (n,m) in N: If (n share nodes with m): E <- E ∪ (n,m) C <- ExtractCommunities(new Graph(N,E)) ExtractCommunities(Graph G) Egos <- EgoNetworks(G) for e in Egos: C = C ∪ LabelPropagation(e) return C 1 1 1 1 1 1 1 2 1 1 1 1

31. Multidimensional Link Prediction Problem: Can we exploit multidimensional and temporal information to increase the precision of well known unsupervised link prediction approaches? Proposed metrics and results: Appendix