mentor_matching function

Optimal Leader/Mentor Matching

Implementes the algorithm described in Valente and Davis (1999)

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

Returns

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.

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.

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)

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. tools:::Rd_expr_doi("10.1177/000271629956600105")