# graph_tool.dynamics.PottsGlauberState#

class graph_tool.dynamics.PottsGlauberState(g, f, w=1, h=0, s=None)[source]#

Glauber dynamics of the Potts model.

Parameters:
gGraph

Graph to be used for the dynamics

flist of lists or two-dimensional numpy.ndarray

Matrix of interactions between spin values, of dimension $$q\times q$$, where $$q$$ is the number of spins.

wEdgePropertyMap or float (optional, default: 1.)

Edge interaction strength. If a scalar is provided, it’s used for all edges.

hVertexPropertyMap or iterable or float (optional, default: 0.)

Vertex local field. If an iterable is provided, it will be used as the field for all vertices. If a scalar is provided, it will be used for all spins values and vertices.

sVertexPropertyMap (optional, default: None)

Initial global state. If not provided, a random state will be chosen.

Notes

This implements the Glauber dynamics of the Potts model [potts-model] on a network.

If a node $$i$$ is updated at time $$t$$, the transition to state $$s_i(t+1) \in \{0,\dots,q-1\}$$ is done with probability

$P(s_i(t+1)|\boldsymbol s(t)) \propto \exp\left(\sum_jA_{ij}w_{ij}f_{s_i(t+1), s_j(t)} + h^{(i)}_{s_i(t+1)}\right)$

References

Examples

>>> g = gt.GraphView(gt.collection.data["polblogs"].copy(), directed=False)
>>> gt.remove_parallel_edges(g)
>>> g = gt.extract_largest_component(g, prune=True)
>>> f = np.eye(4) * 0.1
>>> state = gt.PottsGlauberState(g, f)
>>> ret = state.iterate_async(niter=1000 * g.num_vertices())
>>> gt.graph_draw(g, g.vp.pos, vertex_fill_color=state.s,
...               output="glauber-potts.pdf")
<...> State of a Glauber Potts dynamics with $$q=4$$ on a political blog network.#

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.