Identity and search in social networks
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Transcript of Identity and search in social networks
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Identity and search in social networks
Presented by Pooja Deodhar
Duncan J. Watts, Peter Sheridan Dodds and M. E. J. Newman
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Presentation OutlinePresentation OutlineIntroductionContentions – Social NetworksAlgorithm explanationOur model and Milgram’s findingsFurther ExtensionsApplications
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IntroductionIntroductionSocial 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
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IntroductionIntroductionSmall 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
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IntroductionIntroduction
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
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Source
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IntroductionIntroductionSearchability
◦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
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IntroductionIntroductionLimited hubs in social networksSocial Networks are more like a
peer-to-peer networkNeed for a hierarchical modelSome measure of distance
between individualsCan be based on targets identity,
friends identity, friend’s popularity
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Contentions – Social Contentions – Social NetworksNetworksIndividual 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
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Contentions – Social Contentions – Social NetworksNetworksBreaking down of world into set
of layersTop layer – whole populationLower layers – specific division
into groups
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Contentions – Social Contentions – Social NetworksNetworksSimilarity xij – between individuals i, j xij – Height of the lowest common
ancestor level between i and jIndividuals in same group are at
distance of one from each other
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Contentions – Social Contentions – Social NetworksNetworks
Combined social distance yij = minh xij
In the above figure H = 2In 1st heirarchy, yij = 1 and yjk = 1
in 2nd
But yik = 4 > yij + yjk = 211
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Contentions – Social Contentions – Social NetworksNetworksProbability 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
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Contentions – Social Contentions – Social NetworksNetworksIndividuals hierarchically
partition the social world in more than one way.◦h = 1, …, H hierarchies
Node’s identity is the vector ◦ is position of node i in hierarchy
h.Social distance
hiv
hiv
hij
hij x y min
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Contentions – Social Contentions – Social NetworksNetworksAt 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
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Algorithm ExplanationAlgorithm ExplanationPrincipal 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 ≥ rfor a desired r.
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SearchabilitySearchabilitySearchable networks occupy a
broad region of parameter space <α,H> which are sociologically plausible
Searchability is generic property of social networks
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Algorithm ExplanationAlgorithm ExplanationIn terms of chain length L,
q = (1 - p)L ≥ rL = length of message chainP = message failure probability
From above, L can be obtained by the approximate inequality,
L <= ln r / ln (1 - p)
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Our model and Milgram’s Our model and Milgram’s findingsfindingsAll searchable networks have α > 0, H
> 1Individuals 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
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Searchable NetworksSearchable Networks
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Solid boundary – N=102,400Dot-dash – N=204800Dash – N=409,600p = 0.25, b = 2, g = 100, r = 0.25
at least
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Our model and Milgram’s Our model and Milgram’s findingsfindingsIncreasing 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
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Searchable NetworksSearchable Networks
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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
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Our model and Milgram’s Our model and Milgram’s datadata
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
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Our model and Milgram’s Our model and Milgram’s findingsfindingsComparison 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
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SummarySummarySimple greedy algorithm.Represents properties present
in real social networks:◦Considers local clustering.◦Reflects the notion of locality.
High-level structure + random links.
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Further ExtensionsFurther ExtensionsShould 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?
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ApplicationsApplicationsBroad 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
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