Modelling, Mining, and Searching Networks Graduate Seminar September 2017 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 Networks - Bonato

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

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 Networks - Bonato

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

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 Networks - Bonato

The web graph nodes: web pages edges: links over 60 trillion nodes Networks - Bonato

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

Networks - Bonato

Biological networks: proteomics nodes: proteins edges: biochemical interactions Yeast: 2401 nodes 11000 edges Networks - Bonato

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

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

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

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

6 Dimensions of Separation in Facebook and LinkedIn Networks - Bonato

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 Networks - Bonato

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

Twilight: visualized Networks - Bonato

Twilight: centrality measures Networks - Bonato

Other visualizations: Harry Potter and the Goblet of Fire Networks - Bonato

Other ongoing thesis topics Networks of enemies/rivalry Network visualization Graph learning Networks - Bonato

Cops and Robbers C C R C Networks - Bonato

Cops and Robbers C C R C Networks - Bonato

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

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

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

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). Networks - Bonato

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

Miniconference on the Mathematics of Computation Networks - Bonato

Miniconference on the Mathematics of Computation Networks - Bonato

Miniconference on the Mathematics of Computation Zombie horde up to 𝑛/2 - 2 zombies on an induced path will never capture the survivor Networks - Bonato

Networks - Bonato

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 Networks - Bonato

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 (2010-13) and Associate Dean, YSGS (2013-17) editor-in-Chief of journal Internet Mathematics; editor of Contributions to Discrete Mathematics Ryerson Fellow at Massey College, UT

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