The Seven Bridges of KönigsbergThe Seven Bridges of Königsberg
"I think the next century
the century of complexity”
Network or Graph?
Network often refers to real systems
• 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)
G (V, E ⊆ (V x V))
G (V, E ⊆ (V x V))
G (V, E)
E = (E0, E1, …, Em (V x V))
Points of view
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
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
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)
A social structure,
determined by interactions
between individuals, groups,
Social Networks' Properties
The tendency of individuals to
associate and bond
with similar others
"birds of a feather ﬂock together"
One's emotions, opinions, or behaviors
are affected by others
Social networks transmit states and
behaviors such as obesity, smoking,
drinking and happiness*
Why does it work?
Commitment and Consistency
Can we measure
and maximise inﬂuence?
• Where to place monitoring stations to
• Which are the inﬂuential blogs?
• Which blogs create big cascades?
• Who are the inﬂuencers?
• Where should I advertise?