NMFA

Version 11/25/2021

This is the code repository for the paper "Deciphering the generating rules and functionalities of complex networks"

https://www.nature.com/articles/s41598-021-02203-4

File Structure

├── Tutorial.ipynb          // Quick Start Guide
├── NFD.py                  // Core Function Library
└── README.md

Requirements

• Python 3.6 or higher (If you want to use Networkit, use python 3.7.x)
• Networkx
• Networkit (only for Linux and MacOS according to its official guide)
• tqdm
• scipy

Reference of Core Functions

---

node_dimension_single(G, node, weight=None, fig=True)

Calculate the NFD value of the target node

input

G: (Networkx Graph) - Input graph

weight: (String) - Edge attribute of weight.

node: Label of the target node

output

[1] (double) - NFD value

[2] (double) - r value of linear regression

---

nfd(G, Q = [q/100 for q in range(-2000,2001,10)])

Calculate tau of unweighted network

input

G: (Networkx Graph) - Input graph

Q: (list) - Distortion exponents

output

[1] (numpy.array) - tau_list

---

nfd_nk(G, Q = [q/100 for q in range(-2000,2001,10)])

Calculate tau of unweighted network using networkit package. Much faster but only available on Linux and MacOS

input

G: (Networkx Graph) - Input graph

Q: (list) - Distortion exponents

output

[1] (numpy.array) - tau_list

---

nfd_multiprocess(G, Q = [q/100 for q in range(-2000,2001,10)])

Calculate tau of unweighted network using python built-in Multiprocessing. Much faster but only available on Linux and MacOS

input

G: (Networkx Graph) - Input graph

Q: (list) - Distortion exponents

output

[1] (numpy.array) - tau_list

---

wnfd(G, Q = [q/100 for q in range(-2000,2001,10)], fdigi=3)

Calculate tau of weighted network

input

G: (Networkx Graph) - Input graph

Q: (list) - Distortion exponents

fdigi: (int) - Precision of path length

output

[1] (numpy.array) - tau_list

---

wnfd_nk(G, Q = [q/100 for q in range(-2000,2001,10)], fdigi=3)

Calculate tau of weighted network using networkit package. Much faster but only available on Linux and MacOS

input

G: (Networkx Graph) - Input graph

Q: (list) - Distortion exponents

fdigi: (int) - Precision of path length

output

[1] (numpy.array) - tau_list

---

nspectrum(tau_list,q_list=[q/100 for q in range(-2000,2001,10)],name=None,linewidth=5)

Calculate $\alpha$, $f(\alpha)$ and asymmetry, and draw multifractal spectrum

input

tau_list: (list) - tau

q_list: (list) - Distortion exponents

name: (String) - Name of the network (for legend)

linewidth: (int) - line width in figure

output

[1] (numpy.array) - $\alpha$

[2] (numpy.array) - $f(\alpha)$

[3] (double) - asymmetry

---

ndimension(tau_list,q_list=[q/100 for q in range(-2000,2001,10)],name=None,linewidth=5)

Calculate $D(q)$, and draw generalized fractal dimension

input

tau_list: (list) - tau

q_list: (list) - Distortion exponents

name: (String) - Name of the network (for legend)

linewidth: (int) - line width in figure

output

[1] (numpy.array) - $D(q)$

[2] (numpy.array) - Distortion exponents

---

distance(ndim_list)

Calculate structure distance

input

ndim_list: (list) - $D(q)$

output

[1] (numpy.array) - N by N matrix of structure distance

---

nheat(tau_list, q_list=[q/100 for q in range(-2000,2001,10)])

Calculate specific heat

input

tau_list: (list) - tau

q_list: (list) - Distortion exponents

output

[1] (numpy.array) - Specific heat

[2] (numpy.array) - Distortion exponents