graph_tool.dynamics.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.pdf")
<...>
../_images/binary-threshold.png

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.
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.