Complex Network Analysis

  • 2,587 views
Uploaded on

 

More in: Education , Technology , Design
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
    Be the first to like this
No Downloads

Views

Total Views
2,587
On Slideshare
0
From Embeds
0
Number of Embeds
2

Actions

Shares
Downloads
12
Comments
0
Likes
0

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 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: Erdӧs Number (Paul Erdӧs)
    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-γ
    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