Graduate Seminar
September 2016
Modelling, Mining, and
Searching Networks
Anthony Bonato
Ryerson University
Friendship networks
• network of on- and off-line friends form a large
web of interconnected links
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6 degrees of separation
• (Stanley Milgram,67):
famous chain letter
experiment
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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
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Complex networks in the era of Big Data
• web graph, social networks, biological networks, internet
networks, …
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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
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The web graph
• nodes: web pages
• edges: links
– over 60 trillion
nodes
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Ryerson
Nuit
Blanche
City of
Toronto
Four
Seasons
Hotel
Frommer’s
Greenland
Tourism
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Biological networks: proteomics
nodes: proteins
edges:
biochemical interactions
Yeast:
2401 nodes
11000 edges
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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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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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On-line Social Networks (OSNs)
Facebook, Twitter, LinkedIn, Instagram…
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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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6 Dimensions of Separation in
Facebook and LinkedIn
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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
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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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Twilight: visualized
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Twilight: centrality measures
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Other visualizations:
Harry Potter and the Goblet of Fire
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Cops and Robbers
C
C
R
C
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Cops and Robbers
C
C
R
C
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Cops and Robbers
C
R
C
C
cop number c(G) ≤ 3
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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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Applications of Cops and Robbers
• robotics
– mobile computing
– missile-defense
– gaming
• counter-terrorism
– intercepting messages
or agents
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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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Variants on the classic game
• Seepage
• Wall Cops and Robbers
• Cops, Robbers, and Barricades
• Zombies and Survivors
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Zombie horde
• up to 𝑛/2 - 2
zombies on
an induced
path will
never capture
the survivor
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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
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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
Drop in office hours
• Monday Sept 26, 1-2 pm, Wed Sept 28, 1112 pm, and Thursday Sept 29: 1-2 pm.
• Yeates School of Graduate Studies
• 11th floor of 1 Dundas St West, YDI – 1117
• Come to say hello, chat, discuss thesis topics
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AM8204 – Topics in Discrete
Mathematics
• Winter 2017
• 6 weeks each: complex networks, graph
searching
• project based
• Prequisite: AM8002 (or permission from
me)
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