This vignette describes signed networks and how they are implemented
in the signnet package.
What are signed networks?
Traditional SNA usually deals with relations among entities (e.g. people) that are positive, including “friendship”, “advice seeking”, etc. Most network analytic tools are devised under this premise, be that centrality indices, clustering tools and so forth. But of course not all occurring relations are positive. People can be friends but also foes.
This gives rise to signed networks. These networks are usually composed of both, positive and negative, ties measured among a set of entities. Traditional network analytic tools are not applicable to such networks without adapting for negative ties.
The signnet package brings together methods that have
been developed to analyse signed networks. This includes
Data structures for signed networks in signnet
The foundation of signnet is provided by
igraph. All functions in the package assume that an igraph
object is a signed network if it has an edge attribute “sign” with
values 1 (positive) or -1 (negative).
g <- graph.full(5,directed = FALSE,loops = FALSE)
E(g)$sign <- 1
g
#> IGRAPH 9d65aef U--- 5 10 -- Full graph
#> + attr: name (g/c), loops (g/l), sign (e/n)
#> + edges from 9d65aef:
#> [1] 1--2 1--3 1--4 1--5 2--3 2--4 2--5 3--4 3--5 4--5All methods (should) throw an error if the sign attribute is missing or contains other values than -1 and 1.
Matrices associated with a signed network follow the
igraph naming scheme. The signed adjacency matrix can be
obtained with as_adj_signed().
data("tribes")
as_adj_signed(tribes)[1:5,1:5]
#> Gavev Kotun Ove Alika Nagam
#> Gavev 0 1 -1 -1 -1
#> Kotun 1 0 -1 0 -1
#> Ove -1 -1 0 1 0
#> Alika -1 0 1 0 0
#> Nagam -1 -1 0 0 0The signed Laplacian matrix is obtained by
laplacian_matrix_signed().
laplacian_matrix_signed(tribes)[1:5,1:5]
#> Gavev Kotun Ove Alika Nagam
#> Gavev 8 -1 1 1 1
#> Kotun -1 8 1 0 1
#> Ove 1 1 6 -1 0
#> Alika 1 0 -1 3 0
#> Nagam 1 1 0 0 7Included datasets
The package includes two well known datasets.
The “tribes” dataset is a signed social network of tribes of the Gahuku–Gama alliance structure of the Eastern Central Highlands of New Guinea. The network contains sixteen tribes connected by friendship (“rova”) and enmity (“hina”).
The “cowList” dataset contains a list of 52 signed networks of inter-state relations over time (1946-1999). Two countries are connected by a positive tie if they form an alliance or have a peace treaty. A negative tie exists between countries who are at war or in other kinds of conflicts. The dataset is derrived from the correlates of war.