Naming Games in Social Naming Games in Social NetworksNetworks

Qiming LuQiming LuDept. of Physics, RensselaerDept. of Physics, Rensselaer

György Korniss György Korniss

Dept. of Dept. of Physics, Rensselaer

Boleslaw Szymanski Boleslaw Szymanski

Dept of Computer Science, Rensselaer

Funded by NSF & Rensselaer

23/4/19 Rensselaer Polytechnic Institute 2

Language Games, Semiotic Language Games, Semiotic DynamicsDynamics

Evolution of “language” in artificial or human agents

Artificial and autonomous software agents or robots bootstraping a shared lexicon without human intervention (Steels, 1995)

Collaborative tagging: human web users spontaneously create loose categorization schemes (“folksonomy”). See, e.g., del.icio.us and www.flickr.com (Golder & Huberman, ‘05; Cattuto et al., ‘05 )

Can also be used to identify community structures in complex networks

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Naming (Language) GamesNaming (Language) GamesRules and model description (for a single Rules and model description (for a single object)object)

blah

kefeokoeta

blah

kefeokoetablah

“ speaker”“ listener” “ speaker” “ listener”

failure

blah

kefeokoetablah

blah blah

“ speaker”“ listener” “ speaker” “ listener”

success

Steels (1995)Baronchelli et al. (2005)

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Temporal Behavior in NGTemporal Behavior in NGFully-connected (complete graph) & 2D Fully-connected (complete graph) & 2D regular networkregular network

Total Total number of number of

wordswords

Number of Number of different different

wordswords

Success Success raterate

Baronchelli et al. (2005)

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Temporal Behavior in NGTemporal Behavior in NGRandom Geometric Graphs Random Geometric Graphs (Spatial graph: (Spatial graph: Coarsening)Coarsening)

Total Total number of number of

wordswords

Number of Number of different different

wordswords

Success Success raterate Convergence Convergence

TimeTime

~N~N1.071.07

Lu. et al., ‘06

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Comparison of Average Comparison of Average Consensus TimesConsensus Times

For d<dFor d<d**, d-, d-dimensional dimensional coarsening:coarsening:

2~ Ntc30.1~ Ntc

dc Nt /1~

5.0~:)( NtFCd c

4d

d=1d=1::

d=2d=2::

For d>dFor d>d**, mean-field-, mean-field-like:like:

With:With:

~N~N22

~N~N1.1.

33

~N~N0.50.5

1d-1d-regreg 2d-2d-

regreg

FFCC

2d-SW-2d-SW-RGGRGG

1d 2d(regular or

RGG)

FC(complete

graph)

SW(on 1d or 2d regular or

RGG)

SF(BA)

memory need

per agent

Nw/N

consconst.t.

consconst.t. NN0.50.5 conscons

t.t.conscons

t.t.consensus

time

tcNN22 NN1.11.1 NN0.50.5 NN0.320.32 NN0.400.40

(* or (* or faster)faster)

Baronchelli et al. ’06Dall’Asta et al. ’06Lu. et al., ‘06

2d-RGG2d-RGG

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Naming Game in Social NetworksNaming Game in Social Networks

Prototypical [SW (Watts-Strogatz), SF (Barabási-Albert)] network ensembles have strong self-averaging properties (any single realization almost always resembles a typical one, as opposed to “atypical” but sometimes real-life network topologies)

Many equilibrium and dynamic models on these networks display mean-field features

A more challenging scenario: networks with community structures (Dall’Asta et al.’06)

High-school friendship High-school friendship networks from Add networks from Add Health (Moody 2001)Health (Moody 2001)

(Gonzalez et. al. ’06)

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NG in Social NetworksNG in Social Networkswith strong community structurewith strong community structure

High-school High-school friendship friendship networks networks from Add from Add Health Health (Moody 2001)(Moody 2001)

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NG in Social Networks NG in Social Networks with strong community structurewith strong community structure

Number of Number of different word:different word:

NNdd=1=1NNdd=2=2

NNdd=3=3

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NG in Social NetworksNG in Social Networkswith strong community structurewith strong community structure

High-school High-school friendship friendship networks networks from Add from Add Health Health (Moody 2001)(Moody 2001)

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ConclusionConclusion

The network structure strongly affects the outcome of the agreement dynamics: Coarsening mean-field-like behavior

This simple model can be used to probe and identify the community structure of (social) networks

• Q-state Potts model approach: Kumpula et al. 07

• Lu et al. ‘06 http://arxiv.org/abs/cs/0604075

• Will discuss some more details in our poster