# Sznajd¶

The Sznajd model [1] is a variant of spin model employing the theory of social impact, which takes into account the fact that a group of individuals with the same opinion can influence their neighbours more than one single individual.

In the original model the social network is a 2-dimensional lattice, however we also implemented the variant on any complex networks.

Each agent has an opinion σi = ±1. At each time step, a pair of neighbouring agents is selected and, if their opinion coincides, all their neighbours take that opinion.

The model has been shown to converge to one of the two agreeing stationary states, depending on the initial density of up-spins (transition at 50% density).

## Statuses¶

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1

## Parameters¶

The initial infection status can be defined via:

• fraction_infected: Model Parameter, float in [0, 1]
• Infected: Status Parameter, set of nodes

The two options are mutually exclusive and the latter takes precedence over the former.

## Methods¶

The following class methods are made available to configure, describe and execute the simulation:

### Configure¶

class ndlib.models.opinions.SznajdModel.SznajdModel(graph, seed=None)
SznajdModel.__init__(graph)

Model Constructor

Parameters: graph – A networkx graph object
SznajdModel.set_initial_status(self, configuration)

Set the initial model configuration

Parameters: configuration – a ndlib.models.ModelConfig.Configuration object
SznajdModel.reset(self)

Reset the simulation setting the actual status to the initial configuration.

### Describe¶

SznajdModel.get_info(self)

Describes the current model parameters (nodes, edges, status)

Returns: a dictionary containing for each parameter class the values specified during model configuration
SznajdModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

### Execute Simulation¶

SznajdModel.iteration(self)

Execute a single model iteration

Returns: Iteration_id, Incremental node status (dictionary node->status)
SznajdModel.iteration_bunch(self, bunch_size)

Execute a bunch of model iterations

Parameters: bunch_size – the number of iterations to execute node_status – if the incremental node status has to be returned. progress_bar – whether to display a progress bar, default False a list containing for each iteration a dictionary {“iteration”: iteration_id, “status”: dictionary_node_to_status}

## Example¶

In the code below is shown an example of instantiation and execution of a Sznajd model simulation on a random graph: we set the initial infected node set to the 10% of the overall population.

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.opinions as op

# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)

# Model selection
model = op.SznajdModel(g)
config = mc.Configuration()