1. Modelling, Mining, and Searching Networks Anthony Bonato Ryerson University Graduate Seminar September 2016

2. Friendship networks network of on- and off-line friends form a large web of interconnected links Networks - Bonato

3. 6 degrees of separation (Stanley Milgram,67): famous chain letter experiment Networks - Bonato

4. 4 Degrees in Facebook 1.71 billion users (Backstrom,Boldi,Rosa, Ugander,Vigna,2012) –4 degrees of separation in Facebook –when considering another person in the world, a friend of your friend knows a friend of their friend, on average Networks - Bonato

5. Complex networks in the era of Big Data web graph, social networks, biological networks, internet networks, … Networks - Bonato

6. What is a complex network? no precise definition however, there is general consensus on the following observed properties 1.large scale 2.evolving over time 3.power law degree distributions 4.small world properties Networks - Bonato

7. The web graph nodes: web pages edges: links –over 60 trillion nodes

8. Networks - Bonato Ryerson Greenland Tourism Frommer’s Four Seasons Hotel City of Toronto Nuit Blanche

9. Networks - Bonato

10. Biological networks: proteomics nodes: proteins edges: biochemical interactions Yeast: 2401 nodes 11000 edges

11. Protein networks proteins are essential macromolecules of life understanding their function and role in disease is of importance protein-protein interaction networks (PPI) –nodes: proteins –edges: biochemical interaction Networks - Bonato

12. Domination sets in PPI (Milenkovic, Memisevic, Bonato, Przulj, 2011) dominating sets in graphs we found that dominating sets in PPI networks are vital for normal cellular functioning and signalling –dominating sets capture biologically vital proteins and drug targets –might eventually lead to new drug therapies Networks - Bonato

13. On-line Social Networks (OSNs) Facebook, Twitter, LinkedIn, Instagram…

14. GEO-P model (Bonato et al, 2014): PLOS ONE reverse engineering approach –given network data GEO-P model predicts dimension of an OSN to be around log n, where n is the number of users that is, given the graph structure, we can (theoretically) recover the social space Networks - Bonato

15. 6 Dimensions of Separation in Facebook and LinkedIn Networks - Bonato

16. Character networks cultural work: –fictional works such novels or short stories, movies, biographies, historical works, religious texts character networks: – nodes: characters or persona in a cultural work – edges: co-occurrence Networks - Bonato

17. Social networks in novels joint work with David D’Angelo (Masters candidate) Twilight by Stephanie Meyer Harry Potter and the Goblet of Fire by J.K. Rowlings The Stand by Stephen King Networks - Bonato

18. Twilight: visualized Networks - Bonato

19. Twilight: centrality measures Networks - Bonato

20. Other visualizations: Harry Potter and the Goblet of Fire

21. Cops and Robbers Networks - Bonato C C C R

22. Cops and Robbers Networks - Bonato C C C R

23. Cops and Robbers Networks - Bonato C C C R cop number c(G) ≤ 3

24. Cops and Robbers minimum number of cops needed to capture the robber is the cop number c(G) –well-defined as c(G) ≤ |V(G)| Networks - Bonato

25. Applications of Cops and Robbers robotics –mobile computing –missile-defense –gaming counter-terrorism –intercepting messages or agents Networks - Bonato

26. How big can the cop number be? if the graph G with order n is disconnected, then the cop number can be as n if G is connected, then no one knows how big the cop number can be! Meyniel’s Conjecture: c(G) = O(n 1/2 ). Networks - Bonato

27. Variants on the classic game Seepage Wall Cops and Robbers Cops, Robbers, and Barricades Zombies and Survivors Networks - Bonato

30. Zombie horde Networks - Bonato

32. Thesis topics new models of complex networks biological network models: proteomics, connectomics Banking/financial networks fitting models to data Cops and Robbers games –Meyniel’s conjecture, random graphs, zombies and other variations Networks - Bonato

33. Brief biography over 100 papers, two original books + one in preparation, 7 edited proceedings books, with 65 collaborators (many of which are my students) over 500K lifetime research –grants from NSERC, MITACS, Mprime, and Ryerson –FOS accelerator (aimed just at grad students) supervised 15 masters students, 2 doctoral, and 14 post-docs over 30 invited addresses world-wide (India, China, Europe, North America); most recent: keynote at Oxford University won 2011 and 2009 Ryerson SRC awards for research excellence won 2013 an inaugural YSGS Outstanding Contribution to Graduate Education Award editor-in-Chief of journal Internet Mathematics; editor of Contributions to Discrete Mathematics

34. Drop in office hours Monday Sept 26, 1-2 pm, Wed Sept 28, 11- 12 pm, and Thursday Sept 29: 1-2 pm. Yeates School of Graduate Studies 11 th floor of 1 Dundas St West, YDI – 1117 Come to say hello, chat, discuss thesis topics Networks - Bonato

35. AM8204 – Topics in Discrete Mathematics Winter 2017 6 weeks each: complex networks, graph searching project based Prequisite: AM8002 (or permission from me) Networks - Bonato