Simulating diffusion networks: Using the rdiffnet function

George G. Vega Yon

November 17, 2015

Simulating diffusion networks: Using the rdiffnet function

In 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)
## Diffusion network summary statistics
## Name     : A diffusion network
## Behavior : Random contagion
## -----------------------------------------------------------------------------
##  Period   Adopters   Cum Adopt. (%)   Hazard Rate   Density   Moran's I (sd)  
## -------- ---------- ---------------- ------------- --------- ---------------- 
##        1         20        20 (0.10)             -      0.02 -0.01 (0.00)     
##        2          2        22 (0.11)          0.01      0.02 -0.00 (0.00)     
##        3          2        24 (0.12)          0.01      0.02 -0.00 (0.00)     
##        4          1        25 (0.12)          0.01      0.02 -0.00 (0.00)     
##        5          1        26 (0.13)          0.01      0.02 -0.00 (0.00) *   
##        6          4        30 (0.15)          0.02      0.02  0.00 (0.00) *** 
##        7          1        31 (0.15)          0.01      0.02  0.00 (0.00) *** 
##        8          5        36 (0.18)          0.03      0.02  0.00 (0.00) *** 
##        9          4        40 (0.20)          0.02      0.02  0.01 (0.00) *** 
##       10          5        45 (0.23)          0.03      0.02  0.01 (0.00) *** 
##       11         13        58 (0.29)          0.08      0.02  0.01 (0.00) *** 
##       12         15        73 (0.36)          0.11      0.02  0.02 (0.00) *** 
##       13         21        94 (0.47)          0.17      0.02  0.02 (0.00) *** 
##       14         36       130 (0.65)          0.34      0.02  0.01 (0.00) *** 
##       15         46       176 (0.88)          0.66      0.02  0.00 (0.00) *** 
##       16         23       199 (0.99)          0.96      0.02 -0.01 (0.00)     
##       17          1       200 (1.00)          1.00      0.02               -  
##       18          0       200 (1.00)          0.00      0.02               -  
##       19          0       200 (1.00)          0.00      0.02               -  
##       20          0       200 (1.00)          0.00      0.02               -  
## -----------------------------------------------------------------------------
##  Left censoring  : 0.10 (20)
##  Right centoring : 0.00 (0)
##  # of nodes      : 200
## 
##  Moran's I was computed on contemporaneous autocorrelation using 1/geodesic
##  values. Significane levels  *** <= .01, ** <= .05, * <= .1.

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
## Dynamic network of class -diffnet-
##  Name               : A diffusion network
##  Behavior           : Random contagion
##  # of nodes         : 200 (1, 2, 3, 4, 5, 6, 7, 8, ...)
##  # of time periods  : 20 (1 - 20)
##  Type               : directed
##  Final prevalence   : 1.00
##  Static attributes  : real_threshold (1)
##  Dynamic attributes : -
## Dynamic network of class -diffnet-
##  Name               : A diffusion network
##  Behavior           : Random contagion
##  # of nodes         : 200 (1, 2, 3, 4, 5, 6, 7, 8, ...)
##  # of time periods  : 20 (1 - 20)
##  Type               : directed
##  Final prevalence   : 1.00
##  Static attributes  : real_threshold (1)
##  Dynamic attributes : -
## Dynamic network of class -diffnet-
##  Name               : A diffusion network
##  Behavior           : Random contagion
##  # of nodes         : 200 (1, 2, 3, 4, 5, 6, 7, 8, ...)
##  # of time periods  : 20 (1 - 20)
##  Type               : directed
##  Final prevalence   : 1.00
##  Static attributes  : real_threshold (1)
##  Dynamic attributes : -

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)

Diffusion process

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)")
## Warning in plot_infectsuscep.list(graph$graph, graph$toa, t0, normalize, :
## When applying logscale some observations are missing.

plot_infectsuscep(diffnet_cen, bins=15, K=3, 
                  main = "Distribution of Infectiousness and\nSusceptibility (Central)")
## Warning in plot_infectsuscep.list(graph$graph, graph$toa, t0, normalize, :
## When applying logscale some observations are missing.

plot_infectsuscep(diffnet_mar, bins=15, K=3, 
                  main = "Distribution of Infectiousness and\nSusceptibility (Marginal)")
## Warning in plot_infectsuscep.list(graph$graph, graph$toa, t0, normalize, :
## When applying logscale some observations are missing.