co-evolution of networks and opinions -...
TRANSCRIPT
![Page 1: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/1.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
Co-evolution of networks and opinions
Petter Holme
KTH, CSC, Computational Biology
November 4, 2008, DIMACS
http://www.csc.kth.se/∼pholme/
![Page 2: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/2.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
outline
dynamics of the network
dynamics on the network
![Page 3: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/3.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
outline
dynamics of the network
opinions, information
disease, religion, norms
dynamics on the network
friendships, trust
business contacts
![Page 4: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/4.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
outline
phase transitions in social systems?
our models
verify empirically / experimentally
what can we learn?
![Page 5: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/5.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
outline
phase transitions in social systems?
our models
verify empirically / experimentally
what can we learn?
![Page 6: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/6.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
outline
phase transitions in social systems?
our models
verify empirically / experimentally
what can we learn?
![Page 7: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/7.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
outline
phase transitions in social systems?
our models
verify empirically / experimentally
what can we learn?
![Page 8: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/8.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
outline
phase transitions in social systems?
our models
verify empirically / experimentally
what can we learn?
![Page 9: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/9.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
phase transitions
system’s environmentqu
an
tity
de
scrib
ing
syste
m
![Page 10: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/10.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
. . . in social systems?
quantities describing the system — census statistics,election results, . . .
parameters describing the environment (should be “thesame” for all the agents) — gas price, . . .
does social systems fit this framework?
phase transitions can be categorized by their “criticalexponents”, which depends only on symmetries in thesystem (not boundary conditions, dynamic properties, etc.)
![Page 11: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/11.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
. . . in social systems?
quantities describing the system — census statistics,election results, . . .
parameters describing the environment (should be “thesame” for all the agents) — gas price, . . .
does social systems fit this framework?
phase transitions can be categorized by their “criticalexponents”, which depends only on symmetries in thesystem (not boundary conditions, dynamic properties, etc.)
![Page 12: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/12.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
. . . in social systems?
quantities describing the system — census statistics,election results, . . .
parameters describing the environment (should be “thesame” for all the agents) — gas price, . . .
does social systems fit this framework?
phase transitions can be categorized by their “criticalexponents”, which depends only on symmetries in thesystem (not boundary conditions, dynamic properties, etc.)
![Page 13: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/13.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
. . . in social systems?
quantities describing the system — census statistics,election results, . . .
parameters describing the environment (should be “thesame” for all the agents) — gas price, . . .
does social systems fit this framework?
phase transitions can be categorized by their “criticalexponents”, which depends only on symmetries in thesystem (not boundary conditions, dynamic properties, etc.)
![Page 14: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/14.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
. . . in social systems?
quantities describing the system — census statistics,election results, . . .
parameters describing the environment (should be “thesame” for all the agents) — gas price, . . .
does social systems fit this framework?
phase transitions can be categorized by their “criticalexponents”, which depends only on symmetries in thesystem (not boundary conditions, dynamic properties, etc.)
![Page 15: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/15.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the idea
P. Holme & M. E. J. Newman, Phys. Rev. E 74, 056108 (2006).
Opinions spread over social networks.
People with the same opinion are likely to becomeacquainted.
We try to combine these points into a simple model ofsimultaneous opinion spreading and network evolution.
![Page 16: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/16.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the idea
P. Holme & M. E. J. Newman, Phys. Rev. E 74, 056108 (2006).
Opinions spread over social networks.
People with the same opinion are likely to becomeacquainted.
We try to combine these points into a simple model ofsimultaneous opinion spreading and network evolution.
![Page 17: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/17.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the idea
P. Holme & M. E. J. Newman, Phys. Rev. E 74, 056108 (2006).
Opinions spread over social networks.
People with the same opinion are likely to becomeacquainted.
We try to combine these points into a simple model ofsimultaneous opinion spreading and network evolution.
![Page 18: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/18.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the idea
P. Holme & M. E. J. Newman, Phys. Rev. E 74, 056108 (2006).
Opinions spread over social networks.
People with the same opinion are likely to becomeacquainted.
We try to combine these points into a simple model ofsimultaneous opinion spreading and network evolution.
![Page 19: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/19.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the voter model
Clifford & Sudbury, Biometrika 60, 581 (1973).Holley & Liggett, Ann. Probab. 3, 643 (1975).
![Page 20: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/20.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the voter model
choose one vertex randomly
![Page 21: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/21.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the voter model
copy the opinion of a random neighbor
![Page 22: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/22.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the voter model
and so on . . .
![Page 23: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/23.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the voter model
and so on . . .
![Page 24: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/24.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the voter model
and so on . . .
![Page 25: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/25.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
the voter model
and so on . . .
![Page 26: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/26.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics: precepts
People of similar interests are likely to get acquainted.
The number of edges is constant.
![Page 27: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/27.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics: precepts
People of similar interests are likely to get acquainted.
The number of edges is constant.
![Page 28: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/28.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics: precepts
People of similar interests are likely to get acquainted.
The number of edges is constant.
![Page 29: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/29.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics
![Page 30: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/30.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics
choose one vertex randomly
![Page 31: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/31.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics
rewire an edge to a vertex w same opinion
![Page 32: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/32.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics
and so on . . .
![Page 33: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/33.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics
and so on . . .
![Page 34: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/34.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics
and so on . . .
![Page 35: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/35.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
acquaintance dynamics
and so on . . .
![Page 36: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/36.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
model definition
1 Start with a random network of N vertices M = kN/2edges and G = N/γ randomly assigned opinions.
2 Pick a vertex i at random.3 With a probability φ make an acquaintance formation step
from i.4 . . . otherwise make a voter model step from i.5 If there are edges leading between vertices of different
opinions—iterate from step 2.
![Page 37: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/37.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
model definition
1 Start with a random network of N vertices M = kN/2edges and G = N/γ randomly assigned opinions.
2 Pick a vertex i at random.3 With a probability φ make an acquaintance formation step
from i.4 . . . otherwise make a voter model step from i.5 If there are edges leading between vertices of different
opinions—iterate from step 2.
![Page 38: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/38.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
model definition
1 Start with a random network of N vertices M = kN/2edges and G = N/γ randomly assigned opinions.
2 Pick a vertex i at random.3 With a probability φ make an acquaintance formation step
from i.4 . . . otherwise make a voter model step from i.5 If there are edges leading between vertices of different
opinions—iterate from step 2.
![Page 39: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/39.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
model definition
1 Start with a random network of N vertices M = kN/2edges and G = N/γ randomly assigned opinions.
2 Pick a vertex i at random.3 With a probability φ make an acquaintance formation step
from i.4 . . . otherwise make a voter model step from i.5 If there are edges leading between vertices of different
opinions—iterate from step 2.
![Page 40: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/40.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
model definition
1 Start with a random network of N vertices M = kN/2edges and G = N/γ randomly assigned opinions.
2 Pick a vertex i at random.3 With a probability φ make an acquaintance formation step
from i.4 . . . otherwise make a voter model step from i.5 If there are edges leading between vertices of different
opinions—iterate from step 2.
![Page 41: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/41.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
model definition
1 Start with a random network of N vertices M = kN/2edges and G = N/γ randomly assigned opinions.
2 Pick a vertex i at random.3 With a probability φ make an acquaintance formation step
from i.4 . . . otherwise make a voter model step from i.5 If there are edges leading between vertices of different
opinions—iterate from step 2.
![Page 42: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/42.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
phases
low φ—one dominant cluster
![Page 43: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/43.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
phases
high φ—clusters of similar sizes
![Page 44: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/44.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
quantities we measure
The relative largest size S of a cluster (of vertices with thesame opinion).
The average time τ to reach consensus.
![Page 45: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/45.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
quantities we measure
The relative largest size S of a cluster (of vertices with thesame opinion).
The average time τ to reach consensus.
![Page 46: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/46.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
quantities we measure
The relative largest size S of a cluster (of vertices with thesame opinion).
The average time τ to reach consensus.
![Page 47: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/47.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
cluster size distribution
φ = 0.458
φ = 0.04
φ = 0.96
P(s
)P
(s)
P(s
)
10−4
10−6
10−8
0.01
s
10−4
0.01
10−6
0.01
101 100 1000
10−4
![Page 48: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/48.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
finding the phase transition
Assume a critical scaling form:
scaling form
S = N−a F(Nb(φ − φc)
)
![Page 49: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/49.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
finding the phase transition
40
0
10
20
30
5
6
7
0.45 0.46 0.47
10 0.2 0.4 0.6 0.8φ
S1N−a
φ
S1N−a
![Page 50: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/50.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
finding the phase transition
(φ − φc)Nb
5.0
5.5
6.0
6.5N = 200N = 400
N = 800N = 1600N = 3200
−0.2 0 0.2 0.4
S1N−a
−0.4
a = 0.61 ± 0.05, φc = 0.458 ± 0.008, b = 0.7 ± 0.1random graph percolation: a = b = 1/3
![Page 51: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/51.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
finding the phase transition
(φ − φc)Nb
5.0
5.5
6.0
6.5N = 200N = 400
N = 800N = 1600N = 3200
−0.2 0 0.2 0.4
S1N−a
−0.4
a = 0.61 ± 0.05, φc = 0.458 ± 0.008, b = 0.7 ± 0.1random graph percolation: a = b = 1/3
![Page 52: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/52.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
finding the phase transition
(φ − φc)Nb
5.0
5.5
6.0
6.5N = 200N = 400
N = 800N = 1600N = 3200
−0.2 0 0.2 0.4
S1N−a
−0.4
a = 0.61 ± 0.05, φc = 0.458 ± 0.008, b = 0.7 ± 0.1random graph percolation: a = b = 1/3
![Page 53: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/53.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
dynamic critical behavior
10
15
0.4 0.5
20
0
5
φτN−z
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.75 10.25 0.5φ
Vτ
![Page 54: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/54.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
conclusions
We have proposed a simple, non-equilibrium model for thecoevolution of networks and opinions.
The model undergoes a second order phase transitionbetween: One state of clusters of similar sizes. One statewith one dominant cluster.
The universality class is not the same as random graphpercolation.
In society, a tiny change in the social dynamics may causea large change in the diversity of opinions.
![Page 55: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/55.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
conclusions
We have proposed a simple, non-equilibrium model for thecoevolution of networks and opinions.
The model undergoes a second order phase transitionbetween: One state of clusters of similar sizes. One statewith one dominant cluster.
The universality class is not the same as random graphpercolation.
In society, a tiny change in the social dynamics may causea large change in the diversity of opinions.
![Page 56: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/56.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
conclusions
We have proposed a simple, non-equilibrium model for thecoevolution of networks and opinions.
The model undergoes a second order phase transitionbetween: One state of clusters of similar sizes. One statewith one dominant cluster.
The universality class is not the same as random graphpercolation.
In society, a tiny change in the social dynamics may causea large change in the diversity of opinions.
![Page 57: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/57.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
conclusions
We have proposed a simple, non-equilibrium model for thecoevolution of networks and opinions.
The model undergoes a second order phase transitionbetween: One state of clusters of similar sizes. One statewith one dominant cluster.
The universality class is not the same as random graphpercolation.
In society, a tiny change in the social dynamics may causea large change in the diversity of opinions.
![Page 58: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/58.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
conclusions
We have proposed a simple, non-equilibrium model for thecoevolution of networks and opinions.
The model undergoes a second order phase transitionbetween: One state of clusters of similar sizes. One statewith one dominant cluster.
The universality class is not the same as random graphpercolation.
In society, a tiny change in the social dynamics may causea large change in the diversity of opinions.
![Page 59: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/59.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
an equilibrium model
![Page 60: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/60.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
an equilibrium model
![Page 61: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/61.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
an equilibrium model
![Page 62: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/62.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
an equilibrium model
![Page 63: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/63.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
methodology of mechanistic models
behavior of the individual
model capturingmacroscopic properties
observations
consistent with
![Page 64: Co-evolution of networks and opinions - DIMACSdmac.rutgers.edu/Workshops/Contagion/slides/petter_holme.pdf · Co-evolution of networks and opinions PETTER HOLME phase transitions](https://reader033.vdocuments.net/reader033/viewer/2022051908/5ffc916a819409106025f93d/html5/thumbnails/64.jpg)
Co-evolutionof networks
and opinions
PETTERHOLME
phasetransitions insocialsystems?
coevolution ofnetworks andopinions
validation
thank you!
Mark NewmanZhi-Xi Wu
Gourab GhoshalAndreas GronlundLuıs Enrique Correa da RochaFredrik Liljeros