This function generates networks from the General Temporal model, a generative temporal network model that includes many well-known models such as the Erdős–Rényi model, the Barabási-Albert model or the Bianconi-Barabási model as special cases. This function also includes some flexible mechanisms to vary the number of new nodes and new edges at each time-step in order to generate realistic networks.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
GenerateNet (N,
num_seed = 2 ,
multiple_node = 1 ,
specific_start = NULL ,
m = 1 ,
prob_m = FALSE ,
increase = FALSE ,
log = FALSE ,
noNewNodeStep = NULL ,
m_noNewNodeStep = m ,
custom_PA = NULL ,
mode = 1 ,
alpha = 1 ,
beta = 2 ,
sat_at = 100 ,
offset = 1 ,
mode_f = "gamma",
rate = 0 ,
shape = 0 ,
meanlog = 0 ,
sdlog = 1 ,
scale_pareto = 2 ,
shape_pareto = 2 )
``` |

The parameters can be divided into four groups.

The first group specifies basic properties of the network:

`N` |
Integer. Total number of nodes in the network (including the nodes in the seed graph). Default value is |

`num_seed` |
Integer. The number of nodes of the seed graph (the initial state of the network). The seed graph is a cycle. Default value is |

`multiple_node` |
Positive integer. The number of new nodes at each time-step. Default value is |

`specific_start` |
Positive Integer. If |

The second group specifies the number of new edges at each time-step:

`m` |
Positive integer. The number of edges of each new node. Default value is |

`prob_m` |
Logical. Indicates whether we fix the number of edges of each new node as a constant, or let it follows a Poisson distribution. If |

`increase` |
Logical. Indicates whether we increase the mean of the Poisson distribution over time. If |

`log` |
Logical. Indicates how to increase the mean of the Poisson distribution. If |

`noNewNodeStep` |
Positive integer. The number of time-steps in which no new node is added, while new edges are added between existing nodes. Default value is |

`m_noNewNodeStep` |
Positive integer. The number of new edges in the no-new-node steps. Default value is equal to |

The third group of parameters specifies the preferential attachment function:

`custom_PA` |
Numeric vector. This is the user-input PA function: |

`mode` |
Integer. Indicates the attachment function to be used in generating the network. If |

`alpha` |
Numeric. If |

`beta` |
Numeric. This is the beta in the attachment function |

`sat_at` |
Integer. This is the saturation position |

`offset` |
Numeric. The attachment value of degree |

The final group of parameters specifies the distribution from which node fitnesses are generated:

`mode_f` |
String. Possible values: |

`rate` |
Positive numeric. The rate parameter in the Gamma prior for node fitness. If either rate or shape is |

`shape` |
Positive numeric. The shape parameter in the Gamma prior for node fitness. If either rate or shape is |

`meanlog` |
Numeric. Mean of the log-normal distribution in log scale. Default value is |

`sdlog` |
Positive numeric. Standard deviation of the log-normal distribution in log scale. Default value is |

`scale_pareto` |
Numeric. The scale parameter of the Pareto distribution. Default value is |

`shape_pareto` |
Numeric. The shape parameter of the Pareto distribution. Default value is |

The output is a List contains the following two fields:

`graph` |
a three-column matrix, where each row contains information of one edge, in the form of |

`fitness` |
fitness values of nodes in the network. The name of each value is the ID of the node. |

Thong Pham thongpham@thongpham.net

For subsequent estimation procedures, see `GetStatistics`

.

For simpler functions to generate networks from well-known models, see `Generate_BA`

, `Generate_ER`

, `Generate_BB`

and `Generate_fitonly`

.

1 2 3 4 | ```
library("PAFit")
#Generate a network from the original BA model with alpha = 1, N = 100, m = 1
net <- GenerateNet(N = 100,m = 1,mode = 1, alpha = 1, shape = 0)
str(net)
``` |

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