# Lancichinetti-Fortunato-Radicchi (N_mfl = 301)

This page shows the differences in the dynamics between the microscopic and the kinetic (meanfield) model for Lancichinetti-Fortunato-Radicchi (LFR) type graphs, depending on two parameters:

- $\sigma^2$, which is the variance of the $\beta$ distributions making up the initial distribution $f$,
- $\mu$, the so-called mixing parameter for the construction of the LFR graphs.

### Graphs

μ=0.001 | μ=0.005 | μ=0.01 | μ=0.05 | μ=0.5 |

## $β$ distribution with $σ² = 0.001$

### Movies (ensemble averages)

μ=0.001 | μ=0.005 | μ=0.01 | μ=0.05 | μ=0.5 |
---|---|---|---|---|

plain $w_i$ | plain $w_i$ | plain $w_i$ | plain $w_i$ | plain $w_i$ |

centered $w_i$ | centered $w_i$ | centered $w_i$ | centered $w_i$ | centered $w_i$ |

### Dynamics

Convergence rates are computed over the time span marked in blue in the first plot.

**Parameters:**

- $\mu$: LFR mixing parameter
- $T^*$: time to consensus = $-1/\log(\vert\lambda_2\vert) \cdot \delta t$, where $\lambda_2$ is the second largest eigenvalue of the transition matrix for the associated time discrete model. See here.
- assortativity
- clustering coeff.

### Graph properties

### g(t=0), 1 row per run, p increasing →

1

## $β$ distribution with $σ² = 0.004$

### Movies (ensemble averages)

μ=0.001 | μ=0.005 | μ=0.01 | μ=0.05 | μ=0.5 |
---|---|---|---|---|

plain $w_i$ | plain $w_i$ | plain $w_i$ | plain $w_i$ | plain $w_i$ |

centered $w_i$ | centered $w_i$ | centered $w_i$ | centered $w_i$ | centered $w_i$ |

### Dynamics

Convergence rates are computed over the time span marked in blue in the first plot.

**Parameters:**

- $\mu$: LFR mixing parameter
- $T^*$: time to consensus = $-1/\log(\vert\lambda_2\vert) \cdot \delta t$, where $\lambda_2$ is the second largest eigenvalue of the transition matrix for the associated time discrete model. See here.
- assortativity
- clustering coeff.

### Graph properties

### g(t=0), 1 row per run, p increasing →

1

## $β$ distribution with $σ² = 0.012$

### Movies (ensemble averages)

μ=0.001 | μ=0.005 | μ=0.01 | μ=0.05 | μ=0.5 |
---|---|---|---|---|

plain $w_i$ | plain $w_i$ | plain $w_i$ | plain $w_i$ | plain $w_i$ |

centered $w_i$ | centered $w_i$ | centered $w_i$ | centered $w_i$ | centered $w_i$ |

### Dynamics

Convergence rates are computed over the time span marked in blue in the first plot.

**Parameters:**

- $\mu$: LFR mixing parameter
- $T^*$: time to consensus = $-1/\log(\vert\lambda_2\vert) \cdot \delta t$, where $\lambda_2$ is the second largest eigenvalue of the transition matrix for the associated time discrete model. See here.
- assortativity
- clustering coeff.

### Graph properties

### g(t=0), 1 row per run, p increasing →

1