1. Modelling, Mining, and Searching Networks
Graduate Seminar
September 2017
Modelling, Mining, and Searching Networks
Anthony Bonato
Ryerson University

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
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4. 4 Degrees in Facebook 2 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
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5. Complex networks in the era of Big Data
web graph, social networks, biological networks, internet networks, …
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6. What is a complex network?
no precise definition
however, there is general consensus on the following observed properties
large scale
evolving over time
power law degree distributions
small world properties
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7. The web graph nodes: web pages edges: links over 60 trillion nodes
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8. Nuit Ryerson Blanche City of Toronto Four Seasons Hotel Frommer’s
Greenland
Tourism
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9. Networks - Bonato

10. Biological networks: proteomics
nodes: proteins
edges:
biochemical interactions
Yeast:
2401 nodes
11000 edges
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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
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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
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13. On-line Social Networks (OSNs) Facebook, Twitter, LinkedIn, Instagram…
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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
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15. 6 Dimensions of Separation in Facebook and LinkedIn
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16. Character networks cultural work:
fictional works such novels or short stories, movies, biographies, historical works
character networks:
nodes: characters or persona in a cultural work
edges: co-occurrence
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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
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18. Twilight: visualized
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19. Twilight: centrality measures
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20. Other visualizations: Harry Potter and the Goblet of Fire
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21. Other ongoing thesis topics
Networks of enemies/rivalry
Network visualization
Graph learning
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22. Cops and Robbers C C R C
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23. Cops and Robbers C C R C
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24. Cops and Robbers C R C C
cop number c(G) ≤ 3
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25. 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)|
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26. Applications of Cops and Robbers
robotics
mobile computing
missile-defense
gaming
counter-terrorism
intercepting messages
or agents
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27. 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(n1/2).
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28. Variants on the classic game
Seepage
Wall Cops and Robbers
Cops, Robbers, and Barricades
Zombies and Survivors
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29. Miniconference on the Mathematics of Computation
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30. Miniconference on the Mathematics of Computation
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31. Miniconference on the Mathematics of Computation
Zombie horde
up to 𝑛/2 - 2 zombies on an induced path will never capture the survivor
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32. Networks - Bonato

33. Thesis topics new models of complex networks
biological network models: proteomics, connectomics
Banking/financial networks
fitting models to data/machine learning
Cops and Robbers games
Meyniel’s conjecture, random graphs, zombies and other variations
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34. Brief biography
over 100 papers, three original books, 8 edited proceedings books, with 70 collaborators (many of which are my students)
over 500K lifetime research
grants from NSERC, MITACS, Mprime, and Ryerson
supervised 18 masters students, 4 doctoral, and 15 post-docs
over 30 invited addresses world-wide (India, China, Europe, North America); including 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
Past Dept Chair ( ) and Associate Dean, YSGS ( )
editor-in-Chief of journal Internet Mathematics; editor of Contributions to Discrete Mathematics
Ryerson Fellow at Massey College, UT

35. Drop in office hours Wed Sept 27, 10 – 12 pm ENG ENG 238
Come to say hello, chat, discuss thesis topics
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