Simulation of diffusion networks: rdiffnet
Thomas W. Valente and George G. Vega Yon
Introduction
Before we start, a review of the concepts we will be using here
- Exposure: Proportion/number of neighbors that has adopted an innovation at each point in time.
- Threshold: The proportion/number of your neighbors who had adopted at or one time period before ego (the focal individual) adopted.
- Infectiousness: How much \(i\)’s adoption affects her alters.
- Susceptibility: How much \(i\)’s alters’ adoption affects her.
- Structural equivalence: How similar are \(i\) and \(j\) in terms of position in the network.
Simulating diffusion networks
We will simulate a diffusion network with the following parameters:
- Will have 1,000 vertices,
- Will span 20 time periods,
- The initial adopters (seeds) will be selected random,
- Seeds will be a 10% of the network,
- The graph (network) will be small-world,
- Will use the WS algorithmwith \(p=.2\) (probability of rewire).
- Threshold levels will be uniformly distributed between [0.3, 0.7]
To generate this diffusion network we can use the rdiffnet function included in the package:
# Setting the seed for the RNG
set.seed(1213)
# Generating a random diffusion network
net <- rdiffnet(
n = 1e3, # 1.
t = 20, # 2.
seed.nodes = "random", # 3.
seed.p.adopt = .1, # 4.
seed.graph = "small-world", # 5.
rgraph.args = list(p=.2), # 6.
threshold.dist = function(x) runif(1, .3, .7) # 7.
)The function
rdiffnetgenerates random diffusion networks. Main features:Simulating random graph or using your own,
Setting threshold levels per node,
Network rewiring throughout the simulation, and
Setting the seed nodes.
The simulation algorithm is as follows:
If required, a baseline graph is created,
Set of initial adopters and threshold distribution are established,
The set of t networks is created (if required), and
Simulation starts at t=2, assigning adopters based on exposures and thresholds:
For each \(i \in N\), if its exposure at \(t-1\) is greater than its threshold, then adopts, otherwise continue without change.
next \(i\)
Rumor spreading
library(netdiffuseR)
set.seed(09)
diffnet_rumor <- rdiffnet(
n = 5e2,
t = 5,
seed.graph = "small-world",
rgraph.args = list(k = 4, p = .3),
seed.nodes = "random",
seed.p.adopt = .05,
rewire = TRUE,
threshold.dist = function(i) 1L,
exposure.args = list(normalized = FALSE)
)summary(diffnet_rumor)# Diffusion network summary statistics
# Name : A diffusion network
# Behavior : Random contagion
# -----------------------------------------------------------------------------
# Period Adopters Cum Adopt. (%) Hazard Rate Density Moran's I (sd)
# -------- ---------- ---------------- ------------- --------- ----------------
# 1 25 25 (0.05) - 0.01 -0.00 (0.00)
# 2 78 103 (0.21) 0.16 0.01 0.01 (0.00) ***
# 3 187 290 (0.58) 0.47 0.01 0.01 (0.00) ***
# 4 183 473 (0.95) 0.87 0.01 0.01 (0.00) ***
# 5 27 500 (1.00) 1.00 0.01 -
# -----------------------------------------------------------------------------
# Left censoring : 0.05 (25)
# Right centoring : 0.00 (0)
# # of nodes : 500
#
# Moran's I was computed on contemporaneous autocorrelation using 1/geodesic
# values. Significane levels *** <= .01, ** <= .05, * <= .1.plot_diffnet(diffnet_rumor, slices = c(1, 3, 5))
# We want to use igraph to compute layout
igdf <- diffnet_to_igraph(diffnet_rumor, slices=c(1,2))[[1]]
pos <- igraph::layout_with_drl(igdf)
plot_diffnet2(diffnet_rumor, vertex.size = dgr(diffnet_rumor)[,1], layout=pos)
Difussion
set.seed(09)
diffnet_complex <- rdiffnet(
seed.graph = diffnet_rumor$graph,
seed.nodes = which(diffnet_rumor$toa == 1),
rewire = FALSE,
threshold.dist = function(i) rbeta(1, 3, 10),
name = "Diffusion",
behavior = "Some social behavior"
)plot_adopters(diffnet_rumor, what = "cumadopt", include.legend = FALSE)
plot_adopters(diffnet_complex, bg="tomato", add=TRUE, what = "cumadopt")
legend("topleft", legend = c("Disease", "Complex"), col = c("lightblue", "tomato"),
bty = "n", pch=19)
Mentor Matching
# Finding mentors
mentors <- mentor_matching(diffnet_rumor, 25, lead.ties.method = "random")
# Simulating diffusion with these mentors
set.seed(09)
diffnet_mentored <- rdiffnet(
seed.graph = diffnet_complex,
seed.nodes = which(mentors$`1`$isleader),
rewire = FALSE,
threshold.dist = diffnet_complex[["real_threshold"]],
name = "Diffusion using Mentors"
)
summary(diffnet_mentored)# Diffusion network summary statistics
# Name : Diffusion using Mentors
# Behavior : Random contagion
# -----------------------------------------------------------------------------
# Period Adopters Cum Adopt. (%) Hazard Rate Density Moran's I (sd)
# -------- ---------- ---------------- ------------- --------- ----------------
# 1 25 25 (0.05) - 0.01 -0.00 (0.00)
# 2 92 117 (0.23) 0.19 0.01 0.01 (0.00) ***
# 3 152 269 (0.54) 0.40 0.01 0.01 (0.00) ***
# 4 150 419 (0.84) 0.65 0.01 0.01 (0.00) ***
# 5 73 492 (0.98) 0.90 0.01 -0.00 (0.00) **
# -----------------------------------------------------------------------------
# Left censoring : 0.05 (25)
# Right centoring : 0.02 (8)
# # of nodes : 500
#
# Moran's I was computed on contemporaneous autocorrelation using 1/geodesic
# values. Significane levels *** <= .01, ** <= .05, * <= .1.cumulative_adopt_count(diffnet_complex)# 1 2 3 4 5
# num 25.00 80.00 183.0000 338.0000000 470.0000000
# prop 0.05 0.16 0.3660 0.6760000 0.9400000
# rate 0.00 2.20 1.2875 0.8469945 0.3905325cumulative_adopt_count(diffnet_mentored)# 1 2 3 4 5
# num 25.00 117.000 269.000000 419.0000000 492.0000000
# prop 0.05 0.234 0.538000 0.8380000 0.9840000
# rate 0.00 3.680 1.299145 0.5576208 0.1742243Example by changing threshold
# Simulating a scale-free homophilic network
set.seed(1231)
X <- rep(c(1,1,1,1,1,0,0,0,0,0), 50)
net <- rgraph_ba(t = 499, m=4, eta = X)
# Taking a look in igraph
ig <- igraph::graph_from_adjacency_matrix(net)
plot(ig, vertex.color = c("azure", "tomato")[X+1], vertex.label = NA,
vertex.size = sqrt(dgr(net)))
# Now, simulating a bunch of diffusion processes
nsim <- 500L
ans_1and2 <- vector("list", nsim)
set.seed(223)
for (i in 1:nsim) {
# We just want the cum adopt count
ans_1and2[[i]] <-
cumulative_adopt_count(
rdiffnet(
seed.graph = net,
t = 10,
threshold.dist = sample(1:2, 500L, TRUE),
seed.nodes = "random",
seed.p.adopt = .10,
exposure.args = list(outgoing = FALSE, normalized = FALSE),
rewire = FALSE
)
)
# Are we there yet?
if (!(i %% 50))
message("Simulation ", i," of ", nsim, " done.")
}
# Simulation 50 of 500 done.
# Simulation 100 of 500 done.
# Simulation 150 of 500 done.
# Simulation 200 of 500 done.
# Simulation 250 of 500 done.
# Simulation 300 of 500 done.
# Simulation 350 of 500 done.
# Simulation 400 of 500 done.
# Simulation 450 of 500 done.
# Simulation 500 of 500 done.
# Extracting prop
ans_1and2 <- do.call(rbind, lapply(ans_1and2, "[", i="prop", j=))
ans_2and3 <- vector("list", nsim)
set.seed(223)
for (i in 1:nsim) {
# We just want the cum adopt count
ans_2and3[[i]] <-
cumulative_adopt_count(
rdiffnet(
seed.graph = net,
t = 10,
threshold.dist = sample(2:3, 500L, TRUE),
seed.nodes = "random",
seed.p.adopt = .10,
exposure.args = list(outgoing = FALSE, normalized = FALSE),
rewire = FALSE
)
)
# Are we there yet?
if (!(i %% 50))
message("Simulation ", i," of ", nsim, " done.")
}
# Simulation 50 of 500 done.
# Simulation 100 of 500 done.
# Simulation 150 of 500 done.
# Simulation 200 of 500 done.
# Simulation 250 of 500 done.
# Simulation 300 of 500 done.
# Simulation 350 of 500 done.
# Simulation 400 of 500 done.
# Simulation 450 of 500 done.
# Simulation 500 of 500 done.
ans_2and3 <- do.call(rbind, lapply(ans_2and3, "[", i="prop", j=))This can actually be simplified by using the function rdiffnet_multiple. The following lines of code accomplish the same as the previous code avoiding the for-loop (from the user’s perspective). Besides of the usual parameters passed to rdiffnet, the rdiffnet_multiple function requires R (number of repetitions/simulations), and statistic (a function that returns the statistic of insterst). Optionally, the user may choose to specify the number of clusters to run it in parallel (multiple CPUs):
ans_1and3 <- rdiffnet_multiple(
# Num of sim
R = nsim,
# Statistic
statistic = function(d) cumulative_adopt_count(d)["prop",],
seed.graph = net,
t = 10,
threshold.dist = sample(1:3, 500, TRUE),
seed.nodes = "random",
seed.p.adopt = .1,
rewire = FALSE,
exposure.args = list(outgoing=FALSE, normalized=FALSE),
# Running on 4 cores
ncpus = 4L
)boxplot(ans_1and2, col="ivory", xlab = "Time", ylab = "Threshold")
boxplot(ans_2and3, col="tomato", add=TRUE)
boxplot(t(ans_1and3), col = "steelblue", add=TRUE)
legend(
"topleft",
fill = c("ivory", "tomato", "steelblue"),
legend = c("1/2", "2/3", "1/3"),
title = "Threshold range",
bty ="n"
)
- Example simulating a thousand networks by changing threshold levels. The final prevalence, or hazard as a function of threshold levels.
Problems
- Given the following types of networks: Small-world, Scale-free, Bernoulli, what set of \(n\) initiators maximizes diffusion? (solution script and solution plot)
---
title: "Simulation of diffusion networks: rdiffnet"
author: "Thomas W. Valente and George G. Vega Yon"
---

```{r setup, echo=FALSE, message=FALSE, warning=FALSE}
library(netdiffuseR)
knitr::opts_chunk$set(comment = "#")

```

# Introduction

Before we start, a review of the concepts we will be using here

1. Exposure: Proportion/number of neighbors that has adopted an innovation at each point in time.
2. Threshold: The proportion/number of your neighbors who had adopted at or one time period before ego (the focal individual) adopted.
3. Infectiousness: How much $i$'s adoption affects her alters.
4. Susceptibility: How much $i$'s alters' adoption affects her.
5. Structural equivalence: How similar are $i$ and $j$ in terms of position in the network.

# Simulating diffusion networks

We will simulate a diffusion network with the following parameters:

1.  Will have 1,000 vertices,
2.  Will span 20 time periods,
3.  The initial adopters (seeds) will be selected random,
4.  Seeds will be a 10\% of the network,
5.  The graph (network) will be small-world,
6.  Will use the WS algorithmwith $p=.2$ (probability of rewire).
7.  Threshold levels will be uniformly distributed between [0.3, 0.7\]

To generate this diffusion network we can use the `rdiffnet` function included in the package:


```{r Generating the random graph}
# Setting the seed for the RNG
set.seed(1213)

# Generating a random diffusion network
net <- rdiffnet(
  n              = 1e3,                         # 1.
  t              = 20,                          # 2.
  seed.nodes     = "random",                    # 3.
  seed.p.adopt   = .1,                          # 4.
  seed.graph     = "small-world",               # 5.
  rgraph.args    = list(p=.2),                  # 6.
  threshold.dist = function(x) runif(1, .3, .7) # 7.
  )
```


*   The function `rdiffnet` generates random diffusion networks. Main features:
    
    1.  Simulating random graph or using your own,
    
    2.  Setting threshold levels per node,
    
    3.  Network rewiring throughout the simulation, and
    
    4.  Setting the seed nodes.
    
    
*   The simulation algorithm is as follows:
    
    1.  If required, a baseline graph is created,
    
    2.  Set of initial adopters and threshold distribution are established,
    
    3.  The set of t networks is created (if required), and
    
    4.  Simulation starts at t=2, assigning adopters based on exposures and thresholds:
    
        a.  For each $i \in N$, if its exposure at $t-1$ is greater than its threshold, then 
            adopts, otherwise continue without change.
            
        b.  next $i$
    
# Rumor spreading

```{r sim-rumor}
library(netdiffuseR)

set.seed(09)
diffnet_rumor <- rdiffnet(
  n = 5e2,
  t = 5, 
  seed.graph = "small-world",
  rgraph.args = list(k = 4, p = .3),
  seed.nodes = "random",
  seed.p.adopt = .05,
  rewire = TRUE,
  threshold.dist = function(i) 1L,
  exposure.args = list(normalized = FALSE)
  )
```

```{r summary-rumor}
summary(diffnet_rumor)
```


```{r plot-rumor, fig.align='center', cache=TRUE}
plot_diffnet(diffnet_rumor, slices = c(1, 3, 5))

# We want to use igraph to compute layout
igdf <- diffnet_to_igraph(diffnet_rumor, slices=c(1,2))[[1]]
pos <- igraph::layout_with_drl(igdf)

plot_diffnet2(diffnet_rumor, vertex.size = dgr(diffnet_rumor)[,1], layout=pos)
```


# Difussion

```{r sim-complex}
set.seed(09)
diffnet_complex <- rdiffnet(
  seed.graph = diffnet_rumor$graph,
  seed.nodes = which(diffnet_rumor$toa == 1),
  rewire = FALSE,
  threshold.dist = function(i) rbeta(1, 3, 10),
  name = "Diffusion",
  behavior = "Some social behavior"
)

```

```{r plot-complex-and-disease}
plot_adopters(diffnet_rumor, what = "cumadopt", include.legend = FALSE)
plot_adopters(diffnet_complex, bg="tomato", add=TRUE, what = "cumadopt")
legend("topleft", legend = c("Disease", "Complex"), col = c("lightblue", "tomato"),
       bty = "n", pch=19)
```


# Mentor Matching

```{r mentor-match, cache = TRUE}

# Finding mentors
mentors <- mentor_matching(diffnet_rumor, 25, lead.ties.method = "random")

# Simulating diffusion with these mentors
set.seed(09)
diffnet_mentored <- rdiffnet(
  seed.graph = diffnet_complex,
  seed.nodes = which(mentors$`1`$isleader),
  rewire = FALSE,
  threshold.dist = diffnet_complex[["real_threshold"]],
  name = "Diffusion using Mentors"
)

summary(diffnet_mentored)
```

```{r toa_mat-mentors}
cumulative_adopt_count(diffnet_complex)
cumulative_adopt_count(diffnet_mentored)
```


# Example by changing threshold

```{r sim-sim, cache = TRUE, collapse = TRUE}

# Simulating a scale-free homophilic network
set.seed(1231)
X <- rep(c(1,1,1,1,1,0,0,0,0,0), 50)
net <- rgraph_ba(t = 499, m=4, eta = X)

# Taking a look in igraph
ig  <- igraph::graph_from_adjacency_matrix(net)
plot(ig, vertex.color = c("azure", "tomato")[X+1], vertex.label = NA,
     vertex.size = sqrt(dgr(net)))

# Now, simulating a bunch of diffusion processes
nsim <- 500L
ans_1and2 <- vector("list", nsim)
set.seed(223)
for (i in 1:nsim) {
  # We just want the cum adopt count
  ans_1and2[[i]] <- 
    cumulative_adopt_count(
      rdiffnet(
        seed.graph = net,
        t = 10,
        threshold.dist = sample(1:2, 500L, TRUE),
        seed.nodes = "random",
        seed.p.adopt = .10,
        exposure.args = list(outgoing = FALSE, normalized = FALSE),
        rewire = FALSE
        )
      )
  
  # Are we there yet?
  if (!(i %% 50))
    message("Simulation ", i," of ", nsim, " done.")
}

# Extracting prop
ans_1and2 <- do.call(rbind, lapply(ans_1and2, "[", i="prop", j=))

ans_2and3 <- vector("list", nsim)
set.seed(223)
for (i in 1:nsim) {
  # We just want the cum adopt count
  ans_2and3[[i]] <- 
    cumulative_adopt_count(
      rdiffnet(
        seed.graph = net,
        t = 10,
        threshold.dist = sample(2:3, 500L, TRUE),
        seed.nodes = "random",
        seed.p.adopt = .10,
        exposure.args = list(outgoing = FALSE, normalized = FALSE),
        rewire = FALSE
        )
      )
  
  # Are we there yet?
  if (!(i %% 50))
    message("Simulation ", i," of ", nsim, " done.")
}

ans_2and3 <- do.call(rbind, lapply(ans_2and3, "[", i="prop", j=))
```

This can actually be simplified by using the function `rdiffnet_multiple`. The following lines of code accomplish the same as the previous code avoiding the for-loop (from the user's perspective). Besides of the usual parameters passed to `rdiffnet`, the `rdiffnet_multiple` function requires `R` (number of repetitions/simulations), and `statistic` (a function that returns the statistic of insterst). Optionally, the user may choose to specify the number of clusters to run it in parallel (multiple CPUs):

```{r rdiffnet-multiple}
ans_1and3 <- rdiffnet_multiple(
  # Num of sim
  R              = nsim,
  # Statistic
  statistic      = function(d) cumulative_adopt_count(d)["prop",], 
  seed.graph     = net,
  t              = 10,
  threshold.dist = sample(1:3, 500, TRUE),
  seed.nodes     = "random",
  seed.p.adopt   = .1,
  rewire         = FALSE,
  exposure.args  = list(outgoing=FALSE, normalized=FALSE),
  # Running on 4 cores
  ncpus          = 4L
  )

```

```{r sim-sim-results}
boxplot(ans_1and2, col="ivory", xlab = "Time", ylab = "Threshold")
boxplot(ans_2and3, col="tomato", add=TRUE)
boxplot(t(ans_1and3), col = "steelblue", add=TRUE)
legend(
  "topleft",
  fill = c("ivory", "tomato", "steelblue"),
  legend = c("1/2", "2/3", "1/3"),
  title = "Threshold range",
  bty ="n"
)
```


*   Example simulating a thousand networks by changing threshold levels.
    The final prevalence, or hazard as a function of threshold levels.

# Problems

1.  Given the following types of networks: Small-world, Scale-free, Bernoulli,
    what set of $n$ initiators maximizes diffusion?
    (<a href="sim-solutions.r" target="_blank">solution script</a> and <a href="sim-solutions.png" target="_blank">solution plot</a>)
    


Center for Applied Network Analysis (CANA)