VoterState#

class graph_tool.dynamics.VoterState(g, q=2, r=0.0, s=None)[source]#

Bases: DiscreteStateBase

Generalized q-state voter model dynamics.

Parameters:

gGraph: Graph to be used for the dynamics
qint (optional, default: 2): Number of opinions.
rfloat (optional, default: 0.): Random opinion probability.
sVertexPropertyMap (optional, default: None): Initial global state. If not provided, a random state will be chosen.

Notes

This implements the voter model dynamics [clifford-model-1973] [holley-ergodic-1075] on a network.

If a node \(i\) is updated at time \(t\), the transition probabilities from state \(s_i(t)\) to state \(s_i(t+1)\) are given as follows:

1. With a probability \(r\) one of the \(q\) opinions, \(x\), is chosen uniformly at random, and assigned to \(i\), i.e. \(s_i(t+1) = x\).

2. Otherwise, a random (in-)neighbour \(j\) is chosen. and its opinion is copied, i.e. \(s_i(t+1) = s_j(t)\).

References

[clifford-model-1973]

Clifford, P., Sudbury, A., “A model for spatial conflict”, Biometrika 60, 581–588 (1973). DOI: 10.1093/biomet/60.3.581 [sci-hub, @tor].

[holley-ergodic-1075]

Holley, R. A., Liggett, T. M., “Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model”, Ann. Probab. 3, 643–663 (1975). DOI: 10.1214/aop/1176996306 [sci-hub, @tor].

Examples

>>> g = gt.collection.data["pgp-strong-2009"]
>>> state = gt.VoterState(g, q=4)
>>> x = [[] for r in range(4)]
>>> for t in range(2000):
...     ret = state.iterate_sync()
...     s = state.get_state().fa
...     for r in range(4):
...         x[r].append((s == r).sum())
>>> figure(figsize=(6, 4))
<...>
>>> for r in range(4):
...     plot(x[r], label="Opinion %d" % r)
[...]
>>> xlabel(r"Time")
Text(...)
>>> ylabel(r"Number of nodes")
Text(...)
>>> legend(loc="best")
<...>
>>> tight_layout()
>>> savefig("voter.svg")

../_images/voter.svg — Number of nodes with a given opinion vs. time for a voter model dynamics with \(q=4\) opinions.#

Methods

`copy`()	Return a copy of the state.
`get_active`()	Returns list of "active" nodes, for states where this concept is used.
`get_state`()	Returns the internal `VertexPropertyMap` with the current state.
`iterate_async`([niter])	Updates nodes asynchronously (i.e. single vertex chosen randomly), niter number of times.
`iterate_sync`([niter])	Updates nodes synchronously (i.e. a full "sweep" of all nodes in parallel), niter number of times.
`reset_active`()	Resets list of "active" nodes, for states where this concept is used.
`set_active`(active)	Sets the list of "active" nodes, for states where this concept is used.

copy()#: Return a copy of the state.

get_active()#: Returns list of “active” nodes, for states where this concept is used.

get_state()#: Returns the internal VertexPropertyMap with the current state.

iterate_async(niter=1)#: Updates nodes asynchronously (i.e. single vertex chosen randomly), niter number of times. This function returns the number of nodes that changed state.

iterate_sync(niter=1)#: Updates nodes synchronously (i.e. a full “sweep” of all nodes in parallel), niter number of times. This function returns the number of nodes that changed state.

Parallel implementation.

If enabled during compilation, this algorithm will run in parallel using OpenMP. See the parallel algorithms section for information about how to control several aspects of parallelization.

reset_active()#: Resets list of “active” nodes, for states where this concept is used.

set_active(active)#: Sets the list of “active” nodes, for states where this concept is used.

VoterState

Contents

VoterState#