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