Maryam fazel zarandi
Download
1 / 22

Identity and Search in Social Networks D.J.Watts, P.S. Dodds, M.E.J. Newman - PowerPoint PPT Presentation


  • 106 Views
  • Uploaded on

Maryam Fazel-Zarandi. Identity and Search in Social Networks D.J.Watts, P.S. Dodds, M.E.J. Newman. Outlines. Introduction The Hierarchical Model Discussion. Introduction. Source. Milgram’s Experiment. Short chains of acquaintances exist.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Identity and Search in Social Networks D.J.Watts, P.S. Dodds, M.E.J. Newman' - lance


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Maryam fazel zarandi

Maryam Fazel-Zarandi

Identity and SearchinSocial NetworksD.J.Watts, P.S. Dodds, M.E.J. Newman


Outlines
Outlines

  • Introduction

  • The Hierarchical Model

  • Discussion



Milgram s experiment

Source

Milgram’s Experiment

  • Short chains of acquaintances exist.

  • People are able to findthese chains using only local information.


Results in literature
Results in Literature

  • Connected random networks have short average path lengths:

    xij log(N)

    • N = population size,

    • xij = distance between nodes i and j.


Results in literature1
Results in Literature

  • Kleinberg (2000) demonstrated that emergence of the second phenomenon requires special topological structure.

  • For each node i:

    • local edges d(i,j) ≤ p

    • long-range directed edges

      to q random nodes

      Pr(ij) ~ d(i,j)-a


Results in literature2
Results in Literature

  • If networks have a certain fraction of hubs can also search well.

  • Basic idea: get to hubs first

  • Hubs in social networks are limited.



Hierarchical model why how
Hierarchical Model – Why? How?

  • Basic idea: impose some high-level structure, and fill in details at random.

  • Incorporate identity.

  • Need some measure of distance between individuals.

  • Some possible knowledge:

    • Target's identity, friends' identities, friends' popularity, where the message has been.


Hierarchical network construction
Hierarchical Network Construction

  • xij = the height of the lowest common ancestor

    level between i and j

  • z connections for each node with probability:

    p(x) = ce-αx

Network constructed from template

Hierarchical template for the network


Hierarchical network construction1
Hierarchical Network Construction

  • Individuals hierarchically partition the social world in more than one way.

    • h = 1, …, H hierarchies

  • Identity vector

    • is position of node i in hierarchy h.

  • Social distance:


Directing messages
Directing Messages

  • At each step the holder i of the message passes it to one of its friends who is closest to the target t in terms of social distance.

  • Individuals know the identity vectors of:

    • themselves,

    • their friends,

    • the target.


Expected number of steps
Expected Number of Steps

  • What is the expected number of steps to forward a message from a random source to a random target?

  • Define q as probability of an arbitrary message chain reaching a target.

  • Searchable network: Any network for which

    q≥ r

    for a desired r.


Number of steps results
Number of Steps - Results

  • If message chains fail at each node with probability p, require

    where L = length of message chain.

  • Approximation:

    L ln r / ln (1 - p)

q = (1 - p)L ≥ r


Searchable network regions
Searchable Network Regions

  • In H-αspace

  • p = 0.25, r = 0.05

  • b = 2

  • g = 100, z = 99

  • N=102400

  • N=204800

  • N=409600


Probability of message completion
Probability of Message Completion

  • α = 0 (squares) versus α= 2 (circles)

  • N = 102400

  • q ≥ r

    q < r

r = 0.05


Milgram s data
Milgram's Data

  • N = 108

  • b = 10

  • g = 100

  • z = 300

  • Lmodel 6.7

  • Ldata 6.5

  • α = 1, H = 2



Is this an acceptable model
Is this an acceptable model?

  • Simple greedy algorithm.

  • Represents properties present in real social networks:

    • Considers local clustering.

    • Reflects the notion of locality.

  • High-level structure + random links.


Can the model be extended
Can the Model be Extended?

  • Should we consider other parameters such as friend’s popularity information in addition to homophily?

    • Allow variation in node degrees?

  • Assume correlation between hierarchies?

  • Are all hierarchies equally important?


Applications
Applications

  • Can solutions to sociology problems inform other areas of research?

  • Suggested applications:

    • Construction of peer-to-peer networks.

    • Search in databases.


Thank you any questions

Thank You!Any Questions???