Transcript of Complex Network Analysis
- 1. Complex Network Analysis
- 2. What will you get to know ?
To stop the fire you have to create fire
Why do your friends seem to be more popular than you are
Are we living in a Small World
How do we detect epidemics early
Friendship network in BITS
Behavior in Online Social Networking Sites
How popular is something on DC++
- 3. Complex Networks
Non-trivial real-life networks
Observed in most Social, Biological and Computer
networks.
- 4. The Friendship Paradox
On an average, your friends have more friends than you do
True for all networks (or graphs).
Prominent in real life networks.
- 5. The Small World Phenomenon
Any two persons in the world are connected by at most six links of
acquaintances.
Among Mathematicians: Erds Number (Paul Erds)
Among Actors: Bacon Number (Kevin Bacon)
- 6. http://findthebacon.com/Play.aspx
- 7. Complex Network Analysis
Diameter: Then number of links in the shortest path between
furthest nodes. (Small World)
Average path-length
Degree: Number of links on a particular node(Number of
neighbors)
- 8. Network Density: The ratio of edges in the network to the
max possible number of edges.
Density of a social network with large number of nodes is highly
unlikely to exceed 0.5
- 9. Clustering Coefficient: Likelihood that two associates of a
node are associates themselves
Lies between 0 and 1
Y
X
A
- 10. Centrality Measures (Betweenness): The number of shortest
path that passes through a node.
Synonymous with importance.
Important in study of spreading of forest fires, rumors,
information, epidemics etc.
Revisit Friendship Paradox
- 11. BITSian Friendship Network
- 12. BITSian Friendship Network
Network Density: 0.37
Diameter: 4
Average Path-length: 1.99
Average Clustering Coefficient: 0.51
- 13. Twitter Growth Model
With probability p, a new node(user) enters the network and links
with one existing node.
With probability q = 1-p, an existing user gets linked to an
existing node.
Preferential Selection:
P(deg i -> deg i+1) proportional to (i+constant)
- 14. The Twitter growth model
The rate equations are:
- 15. Formula vs Model Simulation
- 16. Model vs Twitter Data
- 17. Power Law!!!
Degree distribution: n(j) = c.j-
Straight line in log-log plot.
Scale free networks.
Many networks conjectured(and many found) to follow power
law.
Eg.-Online Social Networks, Friendship Network, Collaboration
Network (Movie-Actor, Research-Scientists), World Wide Web,
Protien-Protien Interaction, Airline Networks
Pareto Principle: 80-20 rule.
- 18. DC++ Search Spy
A similar approach can be applied to find out number of searches vs
rank of search query.
query
keyword
- 19. Power Law !!!
- 20. Rank of a keyword (node) = number of nodes with degree
greater than its degree.
The inverse function gives the frequency of a keyword ranked
r:
POWER LAW !!!
- 21. Formula matches with the Real DC++ data