infection(graph, toa, t0 = NULL, normalize = TRUE, K = 1L, r = 0.5, expdiscount = FALSE, valued = getOption("diffnet.valued", FALSE), outgoing = getOption("diffnet.outgoing", TRUE))
susceptibility(graph, toa, t0 = NULL, normalize = TRUE, K = 1L, r = 0.5, expdiscount = FALSE, valued = getOption("diffnet.valued", FALSE), outgoing = getOption("diffnet.outgoing", TRUE))netdiffuseR-graphs).toa_mat.expdiscount=TRUETRUE weights will be considered. Otherwise non-zero values will be replaced by ones.TRUE, computed using outgoing ties.expdiscount=TRUE, $w(k) = (1+r)^(k-1)$, otherwise
it will be $w(k)=k$. Note that when $K=1$, the above formulas are equal to the ones presented
in Valente et al. (2015).normalize=TRUE, is applied by dividing the
resulting number from the infectiousness/susceptibility stat
by the number of individuals who adopted the innovation at
time $t$.Given that node $i$ adopted the innovation in time $t$, its Susceptibility is calculated as follows
$$S_i = \frac{% \sum_{k=1}^K\sum_{j=1}^n x_{ij(t-k+1)}z_{j(t-k)}\times \frac{1}{w_k}}{% \sum_{k=1}^K\sum_{j=1}^n x_{ij(t-k+1)}z_{j(1\leq t \leq t-k)} \times \frac{1}{w_k} }\qquad \mbox{for }i,j=1,\dots,n\quad i\neq j$$
where $x(ij,t-k+1)$ is 1 whenever there's a link from $i$ to $j$ at time $t-k+1$, $z(j,t-k)$ is 1 whenever individual $j$ adopted the innovation at time $t-k$, $z(j, 1<=t<=t-k)$ 1="" is="" whenever="" $j$="" had="" adopted="" the="" innovation="" up="" to="" $t-k$,="" and="" $w(k)$="" discount="" rate="" used="" (see="" below).<="" p="">
Similarly, infectiousness is calculated as follows
$$I_i = \frac{% \sum_{k=1}^K \sum_{j=1}^n x_{ji(t+k-1)}z_{j(t+k)}\times \frac{1}{w_k}}{% \sum_{k=1}^K \sum_{j=1}^n x_{ji(t+k-1)}z_{j(t+k\leq t \leq T)}\times \frac{1}{w_k} }\qquad \mbox{for }i,j=1,\dots,n\quad i\neq j$$
It is worth noticing that, as we can see in the formulas, while susceptibility is from alter to ego, infection is from ego to alter.
When outgoing=FALSE the algorithms are based on incoming edges, this is
the adjacency matrices are transposed swapping the indexes $(i,j)$ by
$(j,i)$. This can be useful for some users.
Finally, by default both are normalized by the number of individuals who
adopted the innovation in time $t-k$. Thus, the resulting formulas,
when normalize=TRUE, can be rewritten as
$$% S_i' = \frac{S_i}{\sum_{k=1}^K\sum_{j=1}^nz_{j(t-k)}\times \frac{1}{w_k}} % \qquad I_i' = \frac{I_i}{\sum_{k=1}^K\sum_{j=1}^nz_{j(t-k)} \times\frac{1}{w_k}}$$
For more details on these measurements, please refer to the vignette titled Time Discounted Infection and Susceptibility.
Myers, D. J. (2000). The Diffusion of Collective Violence: Infectiousness, Susceptibility, and Mass Media Networks. American Journal of Sociology, 106(1), 173–208. https://doi.org/10.1086/303110
plot_infectsuscepOther statistics: classify_adopters,
cumulative_adopt_count, dgr,
ego_variance, exposure,
hazard_rate, moran,
struct_equiv, threshold,
vertex_covariate_dist
# Creating a random dynamic graph
set.seed(943)
graph <- rgraph_er(n=100, t=10)
toa <- sample.int(10, 100, TRUE)
# Computing infection and susceptibility (K=1)
infection(graph, toa)
susceptibility(graph, toa)
# Now with K=4
infection(graph, toa, K=4)
susceptibility(graph, toa, K=4)
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