library(knitr) knitr::opts_chunk$set(fig.width=9, fig.height=6, out.width="600px",fig.align = "center")

`rdiffnet`

functionIn this example we compare 3 different simulations that use the same baseline (seed) network, a scale-free generated via `rgraph_ba`

(Barabasi-Albert) with parameter `m=4`

(number of new ties that each added node includes in the graph). The only difference between the three simulations is that we use a different set of seed adopters, "random", "central" and "marginal". All three cases start with 5% of the network having adopted the innovation.

library(netdiffuseR) s <- 11532 set.seed(s) diffnet_ran <- rdiffnet(200, 20, "random", seed.p.adopt = .1, seed.graph = "small-world", rgraph.args = list(undirected=FALSE, k=4, p=.5), threshold.dist = function(x) 0.3) set.seed(s) diffnet_cen <- rdiffnet(200, 20, "central", seed.p.adopt = .1, seed.graph = "small-world", rgraph.args = list(undirected=FALSE, k=4, p=.5), threshold.dist = function(x) 0.3) set.seed(s) diffnet_mar <- rdiffnet(200, 20, "marginal", seed.p.adopt = .1, seed.graph = "small-world", rgraph.args = list(undirected=FALSE, k=4, p=.5), threshold.dist = function(x) 0.3)

Furthermore, we can take a more detail view of what's going on in each network using the `summary`

method. For example, lets take a look at the marginal network:

```
summary(diffnet_mar)
```

At a first look, printing the networks, we can see that they differ in the number of adopters, as the adoption rate shows:

diffnet_ran; diffnet_cen; diffnet_mar

So, as expected, the network that used central nodes as first adopters is the one that reached the highest adoption rate, 0.95; meanwhile the network that used marginal nodes as seed has the lowest adoption rate, 0.56. Lets compare the set of initial adopters graphically

cols <- c("lightblue","green", "blue") oldpar <- par(no.readonly = TRUE) par(mfcol=c(1,3), mai = c(0, 0, 1, 0), mar = rep(1, 4) + 0.1) set.seed(s);plot(diffnet_ran, main="Random seed") set.seed(s);plot(diffnet_cen, main="Central seed") coords <- set.seed(s);plot(diffnet_mar, main="Marginal seed") par(oldpar)

An interesting way of visualizing the diffusion process is using the `plot_diffnet`

function. In this case, instead of plotting all the 20 periods (networks), we only focus on a subset (henceforth we use the `slices`

argument).

plot_diffnet(diffnet_ran, slices = c(1,4,8,12,16,20), layout=coords)

An easy way to compare these three networks is by checking the cumulative adoption counts, in particular, the proportion. Using the function `plot_adopters`

we can achieve our goal

plot_adopters(diffnet_ran, bg = cols[1], include.legend = FALSE, what="cumadopt") plot_adopters(diffnet_cen, bg = cols[2], add=TRUE, what="cumadopt") plot_adopters(diffnet_mar, bg = cols[3], add=TRUE, what="cumadopt") legend("topleft", bty="n", legend = c("Random","Central", "Marginal"), fill=cols)

Comparing hazard rates we can do the following

plot_hazard(diffnet_ran, ylim=c(0,1), bg=cols[1]) plot_hazard(diffnet_cen, add=TRUE, bg=cols[2]) plot_hazard(diffnet_mar, add=TRUE, bg=cols[3]) legend("topleft", bty="n", legend = c("Random","Central", "Marginal"), fill=cols)

Furthermore, we can calculate infectiousness and susceptibility on each network and see whether both are correlated in each one of the processess.

plot_infectsuscep(diffnet_ran, bins=15, K=3, main = "Distribution of Infectiousness and\nSusceptibility (Random)") plot_infectsuscep(diffnet_cen, bins=15, K=3, main = "Distribution of Infectiousness and\nSusceptibility (Central)") plot_infectsuscep(diffnet_mar, bins=15, K=3, main = "Distribution of Infectiousness and\nSusceptibility (Marginal)")

plot_threshold(diffnet_ran)

`rdiffnet_multiple`

The `rdiffnet_multiple`

is a wrapper of `rdiffnet`

that allows performing simulation studies. In particular, the user can defined a set of shared parameters across simulations and retrieve one or more statistics from each one of them. The followin example is included in the manual of the function:

# Simulating a diffusion process with all the defaults but setting # -seed.nodes- to be random set.seed(1) ans0 <- rdiffnet_multiple(R=50, statistic=function(x) sum(!is.na(x$toa)), n = 100, t = 4, seed.nodes = "random", stop.no.diff=FALSE) # Simulating a diffusion process with all the defaults but setting # -seed.nodes- to be central set.seed(1) ans1 <- rdiffnet_multiple(R=50, statistic=function(x) sum(!is.na(x$toa)), n = 100, t = 4, seed.nodes = "central", stop.no.diff=FALSE) boxplot(cbind(Random = ans0, Central = ans1), main="Distribution of number of adopters in\ndifferent seedscenarios", sub = "(50 simulations each)", ylab="Number of adopters")

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