BinaryThresholdState#

class graph_tool.dynamics.BinaryThresholdState(g, w=1.0, h=0.5, r=0.0, s=None)[source]#

Bases: DiscreteStateBase

Generalized binary threshold dynamics.

Parameters:

gGraph: Graph to be used for the dynamics
wEdgePropertyMap or float (optional, default: 1.): Edge weights. If a scalar is provided, it’s used for all edges.
hfloat (optional, default: .5): Relative threshold value.
rfloat (optional, default: 0.): Input random flip probability.
sVertexPropertyMap (optional, default: None): Initial global state. If not provided, a random state will be chosen.

Notes

This implements a Boolean threshold model on a network.

If a node \(i\) is updated at time \(t\), the transition to state \(s_i(t+1)\) is given by

\[\begin{split}s_i(t+1) = \begin{cases} 1, & \text{ if } \sum_jA_{ij}w_{ij}\hat s_j(t) > h k_i,\\ 0, & \text{ otherwise.} \end{cases}\end{split}\]

where \(k_i=\sum_jA_{ij}\) and \(\hat s_i(t)\) are the flipped inputs sampled with probability

\[P(\hat s_i(t)|s_i(t)) = r^{1-\delta_{\hat s_i(t),s_i(t)}}(1-r)^{\delta_{\hat s_i(t),s_i(t)}}.\]

Examples

>>> g = gt.GraphView(gt.collection.data["polblogs"].copy(), directed=False)
>>> gt.remove_parallel_edges(g)
>>> g = gt.extract_largest_component(g, prune=True)
>>> state = gt.BinaryThresholdState(g, r=0.25)
>>> ret = state.iterate_sync(niter=1000)
>>> gt.graph_draw(g, g.vp.pos, vertex_fill_color=state.s,
...               output="binary-threshold.svg")
<...>

../_images/binary-threshold.svg — State of a binary threshold dynamics on a political blog network.#

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.

BinaryThresholdState

Contents

BinaryThresholdState#