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

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Introduction

More often that liked, one of the biggest barriers for people to use R is getting the data into it.
For this tutorial, we classify graph data as follows:
- Raw R network data: Datasets with edgelist, attributes, survey data, etc.
- Already R data: already read into R using igraph, statnet, etc.
- Graph files: DL, UCINET, pajek, etc.
The netdiffuseR package includes several options to read such data.
This tutorial shows how to use those options (functions) so that the user generates diffnet objects (the core of netdiffuseR).
Importantly, while very useful, diffnet objects is not the only way to use netdiffuseR. Most of the functions can also be used with matrices and arrays.

library(netdiffuseR)
knitr::opts_chunk$set(comment = '#')

Raw network data

We call raw network data to datasets that have a somewhat raw form, for example, edgelists, adjacency matrices, survey nomination data, etc. and need to be read into R.
Usually this datasets are acompained with vertex attribute data.
The issue is how to read it into R and handle it altogether.
Before start, we recommend the user to take a look at the Data input functions included in the utils package (see ?read.table), to the functions included in the foreign package (useful to read from Stata, SPSS, etc.), and to the read_excel function in the readxl package[^excelfiles] for reading excel files into R.

[^excelfiles]: While there are other candidates as the openxlsx package, the readxl package has the nice feature of correctly processing the encoding of the excel files. This is specially important if you are dealing with non ASCII or UTF-8 datasets.

Edge lists

In this section we review the function edgelist_to_adjmat
In general terms, an edgelist is a two column matrix or data frame in which each row represents a tie/link from one node to another.
While the basic structure of edgelists only requires having two columns (usually named ego and alter), edgelists can have more information such as intensity/weight/value of the tie, or a spell/timestamp indicating the time range during which the tie exists.
The function edgelist_to_adjmat supports both weights and spells.

Example 1: Loading a static diffusion network via `as_diffnet`

For this example we will use the fakesurvey and fakeEdgelist datasets. The later was been generated using the fakesurvey dataset, which holds survey information retrieved from 10 different individuals in two different groups. Ties in the fakeEdgelist dataset are valued, and its value coincides with the number of nominatios that each individual in the survey did to each other.

# Loading the datasets
data("fakesurvey")
data("fakeEdgelist")

Taking a look at fakesurvey's group and id column and fakeEdgelist's ego and alter columns the user can tell that the laters have been generated by adding up group*100 with id.

head(fakesurvey[,c("id", "group")])
head(fakeEdgelist)

We will use this information later on to verify the way the data is sorted in the resulting diffnet objects.

To use the as_diffnet function we need at least two objects: a dynamic graph represented as either an array or a list of adjacency matrices, each of size $n\times n$, which in our case will be $10\times 10$, and an integer vector of size $n=10$ which holds each vertex's time of adoption. Lets start by generating the dynamic graph using th edgelist_to_adjmat function:

# Coercing the edgelist to an adjacency matrix
adjmat  <- edgelist_to_adjmat(
  edgelist   = fakeEdgelist[,1:2], # Should be a two column matrix/data.frame
  w          = fakeEdgelist$value, # An optional vector with weights
  undirected = FALSE,              # In this case, the edgelist is directed
  t          = 5)                  # We use this option to make 5 replicas of it

As the function warns, there is an edge that had incomplete information, and further was not used to create the adjacency matrix, the edge 11. If we take a look at that edge, we will see that indeed it had incomplete information on the weight attribute:

fakeEdgelist[11,,drop=FALSE]

In order to address this, if we want to keep the vertex 202, an isolated vertex in the data, we need to fill that value up so that when creating the diffnet object we won't have any problem having more attributes or times of adoption that vertices in the graph.

# Filling the empty data, and checking the outcome
fakeEdgelist[11,"value"] <- 1
fakeEdgelist[11,,drop=FALSE]

# Coercing the edgelist to an adjacency matrix (again)
adjmat  <- edgelist_to_adjmat(
  edgelist   = fakeEdgelist[,1:2], # Should be a two column matrix/data.frame
  w          = fakeEdgelist$value, # An optional vector with weights
  undirected = FALSE,              # In this case, the edgelist is directed
  keep.isolates = TRUE,            # NOTICE THIS NEW ARGUMENT!
  t          = 5)                  # We use this option to make 5 replicas of it

As expected, there is no warning. Furthermore, we have told the function that in case of having isolated vertices to keep them, as is in the case of the edge #11 which has the vertex 202. Since we asked the function to create 5 copies of the adjacency matrix, we have a list of length 5 with adjacency matrices. Lets take a look at the first element of this list:

adjmat[[1]]

As you can see, the edgelist_to_adjmat function kept the vertices labels and included them as dimnames in the matrix.[^sparsemat] Now that our adjacency matrix has the number of elements that we expected, which actually coincides with the number of rows in the fakesurvey dataset, we can create a diffnet object:

[^sparsemat]: Another thing to tell, the matrices stored in adjmat are of class dgCMatrix from the Matrix package, these are Column Compressed Stored sparse matrices and allows saving memory in matrices with many zeros. netdiffuseR routines are based in this class of matrices. Furthermore, to have an idea of how much memory sparse matrices save, while a square matrix of size $5e4\times 5e4$ would need close to 18GB of memory using a regular R matrix, a dgCMatrix of the same size takes around 6MB.

# Coercing the adjacency matrix and edgelist into a diffnet object
diffnet <- as_diffnet(
  graph               = adjmat,         # Passing a dynamic graph
  toa                 = fakesurvey$toa, # This is required
  vertex.static.attrs = fakesurvey      # Is is optional
  )

# Taking a look at the diffnet object
diffnet

Example 2: Loading a static diffusion network via `edgelist_to_diffnet`

Following the previous example, instead of "manually" generating the adjacency matrix and calling the as_diffnet function, we will use the edgelist_to_diffnet function. The most important issue when calling this routine is to have matching ids between the edgelist and the attributes dataset. So before calling the edgelist_to_diffnet function we need to fix the id column in the fakesurvey dataset:[^withfunction]

[^withfunction]: The with function allows simplifying data management in R by allowing to reference columns in a data.frame without having to call the data.frame itself (see ?with).

# Before
fakesurvey$id

# Changing the id
fakesurvey$id <- with(fakesurvey, group*100 + id)

# After
fakesurvey$id

Now that it is fixed, we can call the edgelist_to_diffnet function

diffnet2 <- edgelist_to_diffnet(
  edgelist = fakeEdgelist[,1:2], # Passed to edgelist_to_adjmat
  w        = fakeEdgelist$value, # Passed to edgelist_to_adjmat
  dat      = fakesurvey,        # Data frame with -idvar- and -toavar-
  idvar    = "id",              # Name of the -idvar- in -dat-
  toavar   = "toa",             # Name of the -toavar- in -dat-
  keep.isolates = TRUE          # Passed to edgelist_to_adjmat   
)
diffnet2

As a difference with the previous example, here the algorithm makes sure that the ordering of the dataset and the vertices in the adjacency matrix coincide. The previous example did gave us a correctly sorted diffnet object, but that may not always be the case. Nevertheless, the option id.and.per.vars allows the user providing with the names of the variables in the vertex attribute datasets that hold the ids and time period ids of each observation, so that the function sorts the data before coercing it into diffnet objects. More on this in the following examples.

Survey data: Nomination networks

In this part we review the function survey_to_diffnet
This function can use as input either a longitudinal dataset (which should be in long format, this is, one row per individual and time period), or a cross sectional dataset.
For this example we will use both fakesurvey, which holds cross section data, and fakesurveyDyn, which holds longitudinal data.

Example 3: Cross section diffusion data

We start by taking a look at the data

# Loading the data
data("fakesurvey")
fakesurvey

A couple of important remarks for this dataset. First, each individual in this dataset belongs to a different group, while this is not always the case, survey_to_diffnet allows accounting for this through the groupvar argument. Also, besides of having an isolated vertex, two individuals in the survey nominate people that neither weren't survey nor show in their groups:

fakesurvey[c(4,6),]

So in group one 4 nominates id 6, who does not show in the data, and in group two 6 nominates 3, 4, and 8, also individuals who don't show up in the survey.

While for some researchers nominations of unsurveyed individuals may not be of importance, for some others might be. For such cases, the function has the option of either keeping unsurveyed individuals (so you would get a bigger adjacency matrix), or ignore them and keep only those who were surveyed. For example, if we wanted to keep unsurveyed individuals in the network we would need to set no.unsurveyed = FALSE:

# Coercing the survey data into a diffnet object
diffnet_w_unsurveyed <- survey_to_diffnet(
  dat      = fakesurvey,                # The dataset
  idvar    = "id",                      # Name of the idvar (must be integer)
  netvars  = c("net1", "net2", "net3"), # Vector of names of nomination vars
  toavar   = "toa",                     # Name of the time of adoption var
  groupvar = "group",                   # Name of the group var (OPTIONAL)
  no.unsurveyed = FALSE                 # KEEP OR NOT UNSURVEYED
)
diffnet_w_unsurveyed

# Retrieving nodes ids
nodes(diffnet_w_unsurveyed)

A network spanning 5 time periods with 13 vertices (9 surveyed individuals + 4 unsurveyed individuals). This produces a different result when compared to the case in which me use the default behavior of the function, no.unsurveyed = TRUE:

# Coercing the survey data into a diffnet object
diffnet_wo_unsurveyed <- survey_to_diffnet(
  dat      = fakesurvey,                # The dataset
  idvar    = "id",                      # Name of the idvar (must be integer)
  netvars  = c("net1", "net2", "net3"), # Vector of names of nomination vars
  toavar   = "toa",                     # Name of the time of adoption var
  groupvar = "group"                    # Name of the group var (OPTIONAL)
)
diffnet_wo_unsurveyed

# Retrieving nodes ids
nodes(diffnet_wo_unsurveyed)

Furthermore, we can compare the two diffusion networks by sustracting one from another:

difference <- diffnet_w_unsurveyed - diffnet_wo_unsurveyed
difference

Example 4: Longitudinal diffusion data

In this example we will use dynamic network data, this is, an edgelist with spells and dynamic attributes

# Taking a look at the data
data("fakeDynEdgelist")
head(fakeDynEdgelist)

data("fakesurveyDyn")
head(fakesurveyDyn)

Same as before, we have to make sure the ids are right

# Fixing ids
fakesurveyDyn$id <- with(fakesurveyDyn, group*100 + id)

# An individual who is alone
fakeDynEdgelist[11,"value"] <- 1

diffnet <- edgelist_to_diffnet(
  edgelist = fakeDynEdgelist[,1:2], # As usual, a two column dataset
  w        = fakeDynEdgelist$value, # Here we are using weights
  t0       = fakeDynEdgelist$time,  # An integer vector with starting point of spell
  t1       = fakeDynEdgelist$time,  # An integer vector with the endpoint of spell
  dat      = fakesurveyDyn,         # Attributes dataset
  idvar    = "id",                  
  toavar   = "toa",
  timevar  = "time",
  keep.isolates = TRUE              # Keeping isolates (if there's any)
)

diffnet