complex networks analysis @ universita roma tre
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Complex Networks Analysis
3-6-2013
Università degli Studi Roma Tre
Matteo Moci
@matteomoci
moci@cybion.it
Why?
Complex systems are around us
Complex systems No blueprint
No “master-mind”
Self-organization
Evolution
Adaptation
Behind each complex system
there is a network,
that defines the interactions
between the components
Graph theory: 1735, EulerSocial Network Research: 1930s, Moreno Communication networks/internet: 1960s
Ecological Networks: 1979
History
The Seven Bridges of Königsberg
The Seven Bridges of KönigsbergThe Seven Bridges of Königsberg
What's next?
"I think the next century will be
the century of complexity”S. Hawking
Network or Graph?
Network often refers to real systems
• www,
• social network
• metabolic network.
Language: (Network, node, link)
Graph: mathematical representation of a network
• web graph,
• social graph (a Facebook term)
Language: (Graph, vertex, edge)
Graph Modeling
http://www.flickr.com/photos/visual-telling/8499317469/
Single-relational, un-directed
G (V, E ⊆ (V x V))
Single-relational, un-directed
G (V, E ⊆ (V x V))
friend
friend
friend
Alex
Bob
Carla
Multi-relational, directed
G (V, E)E = (E0, E1, …, Em (V x V))
favourited
watched
follows
watched
Alex
Bob
http://lists.w3.org/Archives/Public/public-rdf-wg/2012Apr/0232.html
Points of view
http://lists.w3.org/Archives/Public/public-rdf-wg/2012Apr/0232.html
Different problems, different models
The choice of the proper network representation determines
our ability to use network theory successfully.
In some cases there is a unique, unambiguous
representation. In other cases,
the representation is by no means unique
The way we assign the links between a group of individuals
will determine the nature of the question we can study
Examples
WWW > directed
Protein Interactions > undirected, unweighted
Collaboration network > undirected or weighted
Mobile phone calls > directed, weighted
Facebook Friendship links > undirected, unweighted.
Most graph databases support a graph data
model, known as property graph
A property graph is a
directed, multi-relational graph
Graph morphisms
http://www.tinkerpop.com/docs/wikidocs/blueprints/2.2.0/Graph-Morphisms.html
Graph properties and measures
Degree distribution P(k)
Average path length <d>
Clustering coefficient C
Types of Networks
Random
Power-law
Scale-free (preferential attachment)
Small-world (small diameter, high clustering)
How does the Web "work"?
How does the Web "work"?• Content analysis (text mining)• Link analysis (e.g. PageRank)
PageRank is an algorithm that assigns a numerical weighting to each element of a set of documents
Importance of a Node
• Degree centrality (# of links)
• Betweenness centrality (# of shortest-paths)
• Closeness centrality (mean distance to neighbours)
• PageRank (P that a random walker visits that node)
Social Networks
A social structure, determined by interactions
between individuals, groups,
organisations
http://www.flickr.com/photos/hanspoldoja/5001818922/
Social Networks' Properties
HomophilySocial Influence
The tendency of individuals to associate and bond with similar others
"birds of a feather flock together"
Homophily
http://www.flickr.com/photos/57574984@N00/81938785/
Social InfluenceOne's emotions, opinions, or behaviors are affected by others
Social networks transmit states and behaviors such as obesity, smoking, drinking and happiness*
* http://www.bmj.com/content/337/bmj.a2338
Social Influence
Why does it work?
Reciprocity
Commitment and Consistency
Social Proof
Authority
Liking
Scarcityhttp://en.wikipedia.org/wiki/Special:BookSources/0321011473
Can we measure and maximise influence?
Goal: "Cascades"
http://www.youtube.com/watch?v=GA8z7f7a2Pk
Disease spreading • Where to place monitoring stations to
detect epidemics?
Blogs• Which are the influential blogs?
• Which blogs create big cascades?
Viral marketing• Who are the influencers?
• Where should I advertise?
http://barabasilab.neu.edu/courses/phys5116/
Influence is related to many aspects!
Thesis:
Sviluppo di un Framework
per il Calcolo dell’Influenza su Twitter
Edoardo Venturini
@edoventurini
Popularity
Activity
http://www.flickr.com/photos/antonioculicigno/8928121349/
Engagement
Topic Relevance
Influence Maximization Problem
NP-CompleteHeuristics• Simulated Annealing
Q&AMatteo Moci
moci@cybion.it@matteomoci
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