mentor_matching: Optimal Leader/Mentor Matching

In srdyal/diffusiontest: Analysis of Diffusion and Contagion Processes on Networks

Optimal Leader/Mentor Matching

Description

Implementes the algorithm described in Valente and Davis (1999)

Usage

mentor_matching(
  graph,
  n,
  cmode = "indegree",
  lead.ties.method = "average",
  geodist.args = list()
)

leader_matching(
  graph,
  n,
  cmode = "indegree",
  lead.ties.method = "average",
  geodist.args = list()
)

## S3 method for class 'diffnet_mentor'
plot(
  x,
  y = NULL,
  vertex.size = "degree",
  minmax.relative.size = getOption("diffnet.minmax.relative.size", c(0.01, 0.04)),
  lead.cols = grDevices::topo.colors(attr(x, "nleaders")),
  vshapes = c(Leader = "square", Follower = "circle"),
  add.legend = TRUE,
  main = "Mentoring Network",
  ...
)

Arguments

graph	Any class of accepted graph format (see netdiffuseR-graphs).
n	Number of leaders
cmode	Passed to dgr.
lead.ties.method	Passed to rank
geodist.args	Passed to approx_geodesic.
x	An object of class diffnet_mentor.
y	Ignored.
vertex.size	Either a numeric scalar or vector of size n, or any of the following values: "indegree", "degree", or "outdegree" (see details).
minmax.relative.size	Passed to rescale_vertex_igraph.
lead.cols	Character vector of length attr(x,"nleaders"). Colors to be applied to each group. (see details)
vshapes	Character scalar of length 2. Shapes to identify leaders (mentors) and followers respectively.
add.legend	Logical scalar. When TRUE generates a legend to distinguish between leaders and followers.
main	Character scalar. Passed to title
...	Further arguments passed to plot.igraph

Details

The algorithm works as follows:

1. Find the top n individuals ranking them by dgr(graph, cmode). The rank is computed by the function rank. Denote this set M.

2. Compute the geodesic matrix.

3. For each v in V do:

   1. Find the mentor m in M such that is closest to v

   2. Were there a tie, choose the mentor that minimizes the average path length from v's direct neighbors to m.

   3. If there are no paths to any member of M, or all have the same average path length to v's neighbors, then assign one randomly.

Plotting is done via the function plot.igraph.

When vertex.size is either of "degree", "indegree", or "outdegree", vertex.size will be replace with dgr(.,cmode = ) so that the vertex size reflects the desired degree.

The argument minmax.relative.size is passed to rescale_vertex_igraph which adjusts vertex.size so that the largest and smallest vertices have a relative size of minmax.relative.size[2] and minmax.relative.size[1] respectively with respect to the x-axis.

Value

An object of class diffnet_mentor and data.frame with the following columns:

name	Character. Labels of the vertices
degree	Numeric. Degree of each vertex in the graph
iselader	Logical. TRUE when the vertex was picked as a leader.
match	Character. The corresponding matched leader.

The object also contains the following attributes:

nleaders

Integer scalar. The resulting number of leaders (could be greater than n)

.

graph

The original graph used to run the algorithm.

References

Valente, T. W., & Davis, R. L. (1999). Accelerating the Diffusion of Innovations Using Opinion Leaders. The ANNALS of the American Academy of Political and Social Science, 566(1), 55–67. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/000271629956600105")}

Examples

# A simple example ----------------------------------------------------------
set.seed(1231)
graph <- rgraph_ws(n=50, k = 4, p = .5)

# Looking for 3 mentors
ans <- mentor_matching(graph, n = 3)

head(ans)
table(ans$match) # We actually got 9 b/c of ties

# Visualizing the mentor network
plot(ans)

srdyal/diffusiontest documentation built on Sept. 2, 2023, 2:49 p.m.