diffudist

Diffusion distance and geometry R package

https://github.com/gbertagnolli/diffudist

Repository

Diffusion distance and geometry R package

README.Rmd

---
output: github_document
---



```{r, echo = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  warn = -1,
  comment = "#>",
  fig.path = "man/figures/"
)
```

# diffudist 


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## Overview

The `diffudist` package provides several functions for evaluating the diffusion distance between nodes of a complex network.

## Installation

```{r, echo = 4:6, eval = FALSE}
# Install from CRAN
install.packages("diffudist")

# Or the development version from GitHub
# install.packages("devtools")
devtools::install_github("gbertagnolli/diffudist")
```

## Usage

Additionally to `diffudist` you will also need the `igraph` package, because the main arguments of the functions in `diffudist` are networks as `igraph` objects.

```{r}
library(diffudist)
library(igraph)
library(ggplot2)
igraph_options(
  vertex.frame.color = "white",
  vertex.color = "#00B4A6",
  label.family = "sans-serif")
```

### Examples

```{r plot-g, fig.width=6, fig.height=6}
N <- 100
g <- sample_pa(N, directed = FALSE)
deg_g <- degree(g)
vertex_labels <- 1:N
vertex_labels[which(deg_g < quantile(deg_g, .9))] <- NA
plot(g, vertex.label = vertex_labels, vertex.size = 6 + 10 * (deg_g - min(deg_g)) / max(deg_g))
```


```{r}
D <- get_distance_matrix(g, tau = 2, type = "Normalized Laplacian", verbose = FALSE)
# or, for short:
# get_DDM(g, tau = 2, type = "Normalized Laplacian", verbose = FALSE)
MERW_Pt <- get_diffusion_probability_matrix(g, tau = 2, type = "MERW")
```

The probability transition matrix returned from `get_diffusion_probability_matrix` (or its shortened version `get_diffu_Pt`) is the matrix $e^{-\tau L_{\text{rw}}}$. The diffusion dynamics is controlled by the specific Laplacian matrix $L_{\text{rw}} = I - T_{\text{rw}}$, where $T_{\text{rw}}$ is the jump matrix of the discrete-time random walk corresponding to our continuous-time dynamics.

Let us check that `MERW_Pt` is an actual stochastic (transition) matrix, i.e., that its rows are probability vectors

```{r}
if (sum(MERW_Pt)  - N > 1e-6) {
  print("MERW_Pt is not a stochastic matrix")
} else {
  print("MERW_Pt is a stochastic matrix")
}
```

Compute diffusion distances from the Probability matrix `MERW_Pt` as follows:

```{r}
if (requireNamespace("parallelDist", quietly = TRUE)) {
  # parallel dist
  D_MERW <- as.matrix(parallelDist::parDist(MERW_Pt))
} else {
  # dist
  D_MERW <- as.matrix(stats::dist(MERW_Pt))
}
```

#### Plot distance matrix

And finally plot the distance matrices (requires `ggplot2` and `ggdengro`)

```{r plot_CRW, fig.width=11, fig.height=7, warning=FALSE}
plot_distance_matrix(D, show_dendro = FALSE) +
  scale_y_discrete(breaks = vertex_labels[!is.na(vertex_labels)])
```

```{r plot_MERW, fig.width=11, fig.height=7}
plot_distance_matrix(D_MERW, show_dendro = FALSE) +
  scale_y_discrete(breaks = vertex_labels[!is.na(vertex_labels)])
```

Adding the hierarchical clustering, i.e., visualising a dendrogram.

```{r plots-with-dendro, fig.width=11, fig.height=7, warning=FALSE}
plot_distance_matrix(D)
plot_distance_matrix(D_MERW)
```


## References

Bertagnolli, G., & De Domenico, M. (2021). _Diffusion geometry of multiplex and interdependent systems_. Physical Review E, 103(4), 042301. [DOI: 10.1103/PhysRevE.103.042301](https://doi.org/10.1103/PhysRevE.103.042301), [arXiv: 2006.13032](https://arxiv.org/abs/2006.13032), [my-website](https://gbertagnolli.github.io/publication/ml-diffusion/).

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