measure_diffusion_node() R function from [manynet]

Measures of nodes in a diffusion

These functions allow measurement of various features of a diffusion process:

node_adoption_time(): Measures the number of time steps until nodes adopt/become infected
node_thresholds(): Measures nodes' thresholds from the amount of exposure they had when they became infected
node_infection_length(): Measures the average length nodes that become infected remain infected in a compartmental model with recovery
node_exposure(): Measures how many exposures nodes have to a given mark


node_adoption_time(diff_model)

node_thresholds(diff_model, normalized = TRUE, lag = 1)

node_recovery(diff_model)

node_exposure(.data, mark, time = 0)

Arguments

diff_model: A valid network diffusion model, as created by as_diffusion() or play_diffusion().
normalized: Logical scalar, whether the centrality scores are normalized. Different denominators are used depending on whether the object is one-mode or two-mode, the type of centrality, and other arguments.
lag: The number of time steps back upon which the thresholds are inferred.
.data: An object of a manynet-consistent class:
- matrix (adjacency or incidence) from {base} R
- edgelist, a data frame from {base} R or tibble from {tibble}
- igraph, from the {igraph} package
- network, from the {network} package
- tbl_graph, from the {tidygraph} package
mark: A valid 'node_mark' object or logical vector (TRUE/FALSE) of length equal to the number of nodes in the network.
time: A time point until which infections/adoptions should be identified. By default time = 0.

Adoption time

node_adoption_time() measures the time units it took until each node became infected. Note that an adoption time of 0 indicates that this was a seed node.

Thresholds

node_thresholds() infers nodes' thresholds based on how much exposure they had when they were infected. This inference is of course imperfect, especially where there is a sudden increase in exposure, but it can be used heuristically. In a threshold model, nodes activate when $\sum_{j:\text{active}} w_{ji} \geq \theta_i$ , where $w$ is some (potentially weighted) matrix, $j$ are some already activated nodes, and $theta$ is some pre-defined threshold value. Where a fractional threshold is used, the equation is $\frac{\sum_{j:\text{active}} w_{ji}}{\sum_{j} w_{ji}} \geq \theta_i$ . That is, $theta$ is now a proportion, and works regardless of whether $w$ is weighted or not.

Infection length

node_infection_length() measures the average length of time that nodes that become infected remain infected in a compartmental model with recovery. Infections that are not concluded by the end of the study period are calculated as infinite.

Exposure

node_exposure() calculates the number of infected/adopting nodes to which each susceptible node is exposed. It usually expects network data and an index or mark (TRUE/FALSE) vector of those nodes which are currently infected, but if a diff_model is supplied instead it will return nodes exposure at $t = 0$ .

Examples


smeg <- generate_smallworld(15, 0.025)
  smeg_diff <- play_diffusion(smeg, recovery = 0.2)
  plot(smeg_diff)
  # To measure when nodes adopted a diffusion/were infected
  (times <- node_adoption_time(smeg_diff))
  # To infer nodes' thresholds
  node_thresholds(smeg_diff)
  # To measure how long each node remains infected for
  node_recovery(smeg_diff)
  # To measure how much exposure nodes have to a given mark
  node_exposure(smeg, mark = c(1,3))
  node_exposure(smeg_diff)

References

On diffusion measures

Valente, Tom W. 1995. Network models of the diffusion of innovations

(2nd ed.). Cresskill N.J.: Hampton Press.

measure_diffusion_node function