# graph_tool.dynamics.MajorityVoterState#

class graph_tool.dynamics.MajorityVoterState(g, q=2, r=0, s=None)[source]#

Generalized q-state majority 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 majority voter model dynamics [oliveira-isotropic-1992] 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, the majority opinion $$x$$ held by all (in-)neighbours of $$i$$ is chosen. In case of a tie between two or more opinions, a random choice between them is made. The chosen opinion is then copied, i.e. $$s_i(t+1) = x$$.

References

de Oliveira, M.J., “Isotropic majority-vote model on a square lattice”, J Stat Phys 66: 273 (1992). DOI: 10.1007/BF01060069 [sci-hub, @tor].

Examples

>>> g = gt.collection.data["pgp-strong-2009"]
>>> state = gt.MajorityVoterState(g, q=4)
>>> x = [[] for r in range(4)]
>>> for t in range(2000):
...     ret = state.iterate_async(niter=g.num_vertices())
...     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("majority-voter.svg") Number of nodes with a given opinion vs. time for a majority voter model dynamics with $$q=4$$ opinions.#

Methods

 Return a copy of the state. Returns list of "active" nodes, for states where this concept is used. Returns the internal VertexPropertyMap with the current state. iterate_async([niter]) Updates nodes asynchronously (i.e. iterate_sync([niter]) Updates nodes synchronously (i.e. Resets 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.

If enabled during compilation, this algorithm runs in parallel (i.e. using more than one thread.)

reset_active()#

Resets list of “active” nodes, for states where this concept is used.