Random graph generators

The package includes three new random graph generators:

• graph_kpartite() creates a random k-partite network.
• sample_coreseq() creates a random graph with given coreness sequence.
• sample_pa_homophilic() creates a preferential attachment graph with two groups of nodes.
• split_graph() sample graph with perfect core-periphery structure

graph_kpartite() can be used to construct a complete k-partite graph. A k-partite graph is a graph with k groups of nodes where no two nodes within the same group are connected but are connected to all other nodes in other groups.

The example below shows a 3-partite graph where each group consists of 5 nodes.

g <- graph_kpartite(n = 15, grp = c(5,5,5))

The function sample_coreseq() is conceptually very similar to the function sample_degseq() in {{igraph}}. Instead of sampling networks with the same degree sequence, sample_coreseq() samples network which have the same k-core decomposition

g1 <- sample_gnp(40,0.1)
kcore1 <- sort(coreness(g1))
g2 <- sample_coreseq(kcore1)
kcore2 <- sort(coreness(g2))
all(kcore1==kcore2)
## [1] TRUE

sample_pa_homophilic() creates a preferential attachment graph with two groups of nodes. The parameter h_ab is used to adjust the probability that an edge between groups occurs. A network is maximally heterophilic if h_ab=1, that is there only exist edges between groups, and maximally homophilic if h_ab=0, that is there only exist edges within groups.

# maximally heterophilic network
sample_pa_homophilic(n = 50, m = 2,minority_fraction = 0.2,h_ab = 1)
# maximally homophilic network
sample_pa_homophilic(n = 50, m = 2,minority_fraction = 0.2,h_ab = 0)

The figure below shows some examples for varying degrees of homophily.

The function split_graph() can be used to create graphs with a perfect core-periphery structure. This means that there are two groups of nodes: One forms a clique (the core: all nodes are pairwise connected) and the other group is only connected to nodes in the core (the periphery: all nodes are pairise disconnected)

In the below example, we create a split graph with 100 nodes and core size 2o (100*0.2)

sg <- split_graph(n = 100,p = 0.3,core = 0.2)

The figure below shows the typical pattern of the adjacency matrix of a split graph.

Analytic functions

The most important analytic functions are

• triad_census_attr() which calculates the triad census with vertex attributes.
• core_periphery() which fits a discrete core periphery model.

set.seed(112)
g <- sample_gnp(20,p = 0.3,directed = TRUE)
# add a vertex attribute
V(g)$type <- rep(1:2,each = 10)
triad_census_attr(g,"type")
##  T003-111  T003-112  T003-122  T003-222  T012-111  T012-121  T012-112  T012-122 
##         8        33        28         7        32        40        31        19 
##  T012-211  T012-221  T012-212  T012-222 T021D-111 T021D-211 T021D-112 T021D-212 
##        27        41        25        26         9        19        19        21 
## T021D-122 T021D-222  T102-111  T102-112  T102-122  T102-211  T102-212  T102-222 
##         7        10        11        18        16         5        19        10 
## T021C-111 T021C-211 T021C-121 T021C-221 T021C-112 T021C-212 T021C-122 T021C-222 
##        17        23        29        17        19         7        24        10 
## T111U-111 T111U-121 T111U-112 T111U-122 T111U-211 T111U-221 T111U-212 T111U-222 
##         9        16         7        21         5        13        10         6 
## T021U-111 T021U-112 T021U-122 T021U-211 T021U-212 T021U-222 T030T-111 T030T-121 
##        11        19        13         3        14         7        11        11 
## T030T-112 T030T-122 T030T-211 T030T-221 T030T-212 T030T-222 T120U-111 T120U-112 
##        11        13        10        14         8         5         1         8 
## T120U-122 T120U-211 T120U-212 T120U-222 T111D-111 T111D-121 T111D-112 T111D-122 
##         6         0         4         4         4        12         8        13 
## T111D-211 T111D-221 T111D-212 T111D-222  T201-111  T201-112  T201-121  T201-122 
##        14        20        10        15         0         5         3         5 
##  T201-221  T201-222 T030C-111 T030C-112 T030C-122 T030C-222 T120C-111 T120C-121 
##         3         3         2        12        14         3         3         8 
## T120C-211 T120C-221 T120C-112 T120C-122 T120C-212 T120C-222 T120D-111 T120D-112 
##         7         5         5         7         7         6         0         9 
## T120D-211 T120D-212 T120D-122 T120D-222  T210-111  T210-121  T210-211  T210-221 
##         1         9         4         1         2         8         3         5 
##  T210-112  T210-122  T210-212  T210-222  T300-111  T300-112  T300-122  T300-222 
##         1         3         5         5         0         1         0         2

The output is a named vector where the names are of the form Txxx-abc, where xxx corresponds to the standard triad census notation and “abc” are the attributes of the involved nodes.

The function core_periphery() fits a standard discrete core-periphery model to the data

#graph with perfect core-periphery structure
core_graph <- split_graph(n = 100, p = 0.3, core = 0.2)
core_periphery(core_graph)
## $vec
##   [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 
## $corr
## [1] 1
# random graphs have a very weak core-periphery structure 
rgraph <- sample_gnp(n = 100,p = 0.2)
core_periphery(rgraph)
## $vec
##   [1] 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0
##  [38] 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0
##  [75] 1 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0
## 
## $corr
## [1] 0.162141

More advanced core-periphery models are planned for a future release.

A new print method

I also extended str to work with igraph objects for an alternative way of printing igraph objects using additional information.

library(networkdata)
data("greys")
str(greys)
## -----------------------------------------------------------
## UNNAMED NETWORK (undirected, unweighted, one-mode network)
## -----------------------------------------------------------
## Nodes: 54, Edges: 57, Density: 0.0398, Components: 4, Isolates: 0
## -Vertex Attributes:
##  name(c): Addison Montgomery, Adele Webber, Teddy Altman, Amelia ...
##  sex(c): F, F, F, F, F, F, M, F, M, M, F, M, M, M, F, M, F, F, M, F, M, ...
##  race(c): White, Black, White, White, White, White, Black, Black, Black, ...
##  birthyear(n): 1967, 1949, 1969, 1981, 1976, 1975, 1981, 1969, 1972, ...
##  position(c): Attending, Non-Staff, Attending, Attending, Attending, ...
##  season(n): 1, 2, 6, 7, 5, 3, 6, 1, 6, 7, 8, 3, 2, 1, 1, 2, 1, 2, 1, 1, ...
##  sign(c): Libra, Leo, Pisces, Libra, Leo, Gemini, Leo, Virgo, Aquarius, ...
## ---
## -Edges (first 10): 
##  Arizona Robbins->Leah Murphy Alex Karev->Leah Murphy Arizona
## Robbins->Lauren Boswell Arizona Robbins->Callie Torres Erica
## Hahn->Callie Torres Alex Karev->Callie Torres Mark Sloan->Callie Torres
## George O'Malley->Callie Torres Izzie Stevens->George O'Malley Meredith
## Grey->George O'Malley