This function generates networks from the General Temporal model, a generative temporal network model that includes many well-known models such as the Barabasi-Albert model or the fitness model as special cases. The number of edges of the new node at each time-step can be specified to be fixed, or followed a Poisson distribution. In the latter case, the mean of the Poisson distribution is either held fixed or increased with time.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
GenerateNet (N,
num_seed = 2 ,
multiple_node = 1 ,
specific_start = NULL ,
m = 1 ,
prob_m = FALSE ,
increase = FALSE ,
log = FALSE ,
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 |

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 sat_at in the attachment function |

`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

1. Pham, T., Sheridan, P. & Shimodaira, H. (2016). Nonparametric Estimation of the Preferential Attachment Function in Complex Networks: Evidence of Deviations from Log Linearity, Proceedings of ECCS 2014, 141-153 (Springer International Publishing) (http://dx.doi.org/10.1007/978-3-319-29228-1_13).

2. Pham, T., Sheridan, P. & Shimodaira, H. (2015). PAFit: A Statistical Method for Measuring Preferential Attachment in Temporal Complex Networks. PLoS ONE 10(9): e0137796. doi:10.1371/journal.pone.0137796 (http://dx.doi.org/10.1371/journal.pone.0137796).

3. Pham, T., Sheridan, P. & Shimodaira, H. (2016). Joint Estimation of Preferential Attachment and Node Fitness in Growing Complex Networks. Scientific Reports 6, Article number: 32558. doi:10.1038/srep32558 (www.nature.com/articles/srep32558).

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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