Seminar-Pooja

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					Identity and search in social
networks
   Duncan J. Watts, Peter Sheridan Dodds and M.
   E. J. Newman




                                    Presented by
                                    Pooja Deodhar
Presentation Outline
 Introduction
 Contentions – Social Networks
 Algorithm explanation
 Our model and Milgram’s findings
 Further Extensions
 Applications




                                     2
Introduction
 Social Networks are “Searchable”
 Our model offers explanation of
  searchability in terms of recognizable
  personal identities
 Personal identities - sets of characteristics
  in different social dimensions
 Class of searchable networks and method
  for searching them applicable to many real
  world problems
                                              3
Introduction
   Small World Network
    ◦ Network in which most nodes are not
      neighbors of each other but most nodes can
      be reached from every other node by a
      number of hops




                                                   4
Introduction
Source




   Milgram’s Experiment
    ◦ Short paths exist between individuals in large social
      network
    ◦ Ordinary people can find these short paths
    ◦ People rarely have more than local knowledge about the
      network

                                                               5
Introduction
   Searchability
    ◦ Property of being able to find a target quickly
   Shown to exist in networks
    ◦ With certain fraction of hubs (highly
      connected nodes which once reached can
      distribute messages to all parts of the
      network)
    ◦ Built upon underlying geometric lattice



                                                        6
Introduction
 Limited hubs in social networks
 Social Networks are more like a peer-to-
  peer network
 Need for a hierarchical model
 Some measure of distance between
  individuals
 Can be based on targets identity, friends
  identity, friend’s popularity

                                              7
Contentions – Social Networks
 Individual identities – sets of
  characteristics attributed to them by
  virtue of association, participation in
  social groups
 Groups – Collection of individuals with
  well-defined set of social characteristics




                                               8
Contentions – Social Networks
 Breaking down of world into set of layers
 Top layer – whole population
 Lower layers – specific division into
  groups




                                              9
Contentions – Social Networks
 Similarity xij – between individuals i, j
 xij – Height of the lowest common
  ancestor level between i and j
 Individuals in same group are at distance
  of one from each other




                                              10
Contentions – Social Networks




 Combined social distance yij = minh xij
 In the above figure H = 2
 In 1st heirarchy, yij = 1 and yjk = 1 in 2nd
 But yik = 4 > yij + yjk = 2
                                                 11
Contentions – Social Networks
 Probability of acquaintance between i and
  j decreases with decreasing similarity of
  groups to which they belong
 Link distance x for individual i has
  probability
                  p(x) = ce-αx
 Measure of homophily – tendency of like
  to associate with like

                                              12
Contentions – Social Networks
   Individuals hierarchically partition the
    social world in more than one way.
    ◦ h = 1, …, H hierarchies
   Node’s identity is the vector            v ih
    ◦   v ih is   position of node i in hierarchy h.
   Social distance
                      yij  min x  h
                                  ij
                              h




                                                       13
Contentions – Social Networks
 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
   Two kinds of partial information – social
    distance and network paths
                                                14
Algorithm Explanation
 Principal objective – determine conditions
  for average path length L of a message
  chain is small
 Define q as probability of an arbitrary
  message chain reaching a target.
 Searchable network - Any network for
  which
                     q≥r
  for a desired r.
                                           15
Searchability
 Searchable networks occupy a broad
  region of parameter space <α,H> which
  are sociologically plausible
 Searchability is generic property of social
  networks




                                                16
Algorithm Explanation
   In terms of chain length L,
                 q = (1 - p)L ≥ r
     L = length of message chain
     P = message failure probability
   From above, L can be obtained by the
    approximate inequality,
             L <= ln r / ln (1 - p)



                                           17
Our model and Milgram’s findings
 All searchable networks have α > 0, H > 1
 Individuals are essentially homophilous
  but judge similarity along more than one
  social dimension
 Best performance is achieved for H = 2
  or 3
 Thus, use of 2 or 3 dimensions used by
  individuals in small world experiments
  when forwarding a message
                                          18
Searchable Networks




 Solid boundary – N=102,400
 Dot-dash – N=204800
 Dash – N=409,600
 p = 0.25, b = 2, g = 100, r = 0.25 at least

                                                19
Our model and Milgram’s findings
 Increasing number of independent
  dimensions from H = 1 yields dramatic
  reduction in delivery time for α > 0
 This improvement lost as H is increased
  further
 Thus, network ties become less correlated
  as H increases
 For large H, network becomes a random
  graph, search algorithm becomes random
  walk

                                              20
Searchable Networks




 Probability of message completion when
  for α = 0 (squares) and for α = 2 (circles)
  for N = 102,400
 Horizontal line – pos of the threshold
 Open symbols indicate network is
  searchable – q <= r
                                                21
Our model and Milgram’s data




   n(L) – no. of completed chains of length L
    taken from original small world expt. (shown
    by bar graphs)
   Taken for example of our model for N =
    10^8 individuals and for 42 completed chains
    shown by filled circles
                                               22
Our model and Milgram’s findings
 Comparison of distribution of chain
  lengths in our model with that of Travers
  and Milgram
 Avg. chain length for Milgrams expt = 6.5
 Avg. chain length for our model = 6.7




                                              23
Summary
 Simple  greedy algorithm.
 Represents properties present in real
  social networks:
 ◦ Considers local clustering.
 ◦ Reflects the notion of locality.
 High-level   structure + random links.



                                           24
Further Extensions
 Shouldwe 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?
                                             25
Applications
   Broad class of decentralized problems
    ◦ Peer to peer networking
 Any data structure in which data
  elements can be judged along more than
  one dimension
 Designing of databases
    ◦ Eg. Music files – same genre/same year



                                               26

				
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posted:8/18/2012
language:English
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