Calculate node and edge centrality — centrality • tidygraph

The centrality of a node measures the importance of node in the network. As the concept of importance is ill-defined and dependent on the network and the questions under consideration, many centrality measures exist. tidygraph provides a consistent set of wrappers for all the centrality measures implemented in igraph for use inside dplyr::mutate() and other relevant verbs. All functions provided by tidygraph have a consistent naming scheme and automatically calls the function on the graph, returning a vector with measures ready to be added to the node data. Further tidygraph provides access to the netrankr engine for centrality calculations and define a number of centrality measures based on that, as well as provide a manual mode for specifying more-or-less any centrality score. These measures all only work on undirected graphs.

centrality_alpha(
  weights = NULL,
  alpha = 1,
  exo = 1,
  tol = 1e-07,
  loops = FALSE
)

centrality_authority(weights = NULL, scale = TRUE, options = arpack_defaults())

centrality_betweenness(
  weights = NULL,
  directed = TRUE,
  cutoff = -1,
  normalized = FALSE
)

centrality_power(exponent = 1, rescale = FALSE, tol = 1e-07, loops = FALSE)

centrality_closeness(
  weights = NULL,
  mode = "out",
  normalized = FALSE,
  cutoff = NULL
)

centrality_eigen(
  weights = NULL,
  directed = FALSE,
  scale = TRUE,
  options = arpack_defaults()
)

centrality_hub(weights = NULL, scale = TRUE, options = arpack_defaults())

centrality_pagerank(
  weights = NULL,
  directed = TRUE,
  damping = 0.85,
  personalized = NULL
)

centrality_subgraph(loops = FALSE)

centrality_degree(
  weights = NULL,
  mode = "out",
  loops = TRUE,
  normalized = FALSE
)

centrality_edge_betweenness(weights = NULL, directed = TRUE, cutoff = NULL)

centrality_harmonic(
  weights = NULL,
  mode = "out",
  normalized = FALSE,
  cutoff = NULL
)

centrality_manual(relation = "dist_sp", aggregation = "sum", ...)

centrality_closeness_harmonic()

centrality_closeness_residual()

centrality_closeness_generalised(alpha)

centrality_integration()

centrality_communicability()

centrality_communicability_odd()

centrality_communicability_even()

centrality_subgraph_odd()

centrality_subgraph_even()

centrality_katz(alpha = NULL)

centrality_betweenness_network(netflowmode = "raw")

centrality_betweenness_current()

centrality_betweenness_communicability()

centrality_betweenness_rsp_simple(rspxparam = 1)

centrality_betweenness_rsp_net(rspxparam = 1)

centrality_information()

centrality_decay(alpha = 1)

centrality_random_walk()

centrality_expected()

Arguments

weights: The weight of the edges to use for the calculation. Will be evaluated in the context of the edge data.
alpha: Relative importance of endogenous vs exogenous factors (centrality_alpha), the exponent to the power transformation of the distance metric (centrality_closeness_generalised), the base of power transformation (centrality_decay), or the attenuation factor (centrality_katz)
exo: The exogenous factors of the nodes. Either a scalar or a number number for each node. Evaluated in the context of the node data.
tol: Tolerance for near-singularities during matrix inversion
loops: Should loops be included in the calculation
scale: Should the output be scaled between 0 and 1
options: Settings passed on to igraph::arpack()
directed: Should direction of edges be used for the calculations
cutoff: maximum path length to use during calculations
normalized: Should the output be normalized
exponent: The decay rate for the Bonacich power centrality
rescale: Should the output be scaled to sum up to 1
mode: How should edges be followed. Ignored for undirected graphs
damping: The damping factor of the page rank algorithm
personalized: The probability of jumping to a node when abandoning a random walk. Evaluated in the context of the node data.
relation: The indirect relation measure type to be used in netrankr::indirect_relations
aggregation: The aggregation type to use on the indirect relations to be used in netrankr::aggregate_positions
...: Arguments to pass on to netrankr::indirect_relations
netflowmode: The return type of the network flow distance, either 'raw' or 'frac'
rspxparam: inverse temperature parameter

Value

A numeric vector giving the centrality measure of each node.

Functions

centrality_alpha(): Wrapper for igraph::alpha_centrality()
centrality_authority(): Wrapper for igraph::authority_score()
centrality_betweenness(): Wrapper for igraph::betweenness()
centrality_power(): Wrapper for igraph::power_centrality()
centrality_closeness(): Wrapper for igraph::closeness()
centrality_eigen(): Wrapper for igraph::eigen_centrality()
centrality_hub(): Wrapper for igraph::hub_score()
centrality_pagerank(): Wrapper for igraph::page_rank()
centrality_subgraph(): Wrapper for igraph::subgraph_centrality()
centrality_degree(): Wrapper for igraph::degree() and igraph::strength()
centrality_edge_betweenness(): Wrapper for igraph::edge_betweenness()
centrality_harmonic(): Wrapper for igraph::harmonic_centrality()
centrality_manual(): Manually specify your centrality score using the netrankr framework (netrankr)
centrality_closeness_harmonic(): centrality based on inverse shortest path (netrankr)
centrality_closeness_residual(): centrality based on 2-to-the-power-of negative shortest path (netrankr)
centrality_closeness_generalised(): centrality based on alpha-to-the-power-of negative shortest path (netrankr)
centrality_integration(): centrality based on \(1 - (x - 1)/max(x)\) transformation of shortest path (netrankr)
centrality_communicability(): centrality an exponential tranformation of walk counts (netrankr)
centrality_communicability_odd(): centrality an exponential tranformation of odd walk counts (netrankr)
centrality_communicability_even(): centrality an exponential tranformation of even walk counts (netrankr)
centrality_subgraph_odd(): subgraph centrality based on odd walk counts (netrankr)
centrality_subgraph_even(): subgraph centrality based on even walk counts (netrankr)
centrality_katz(): centrality based on walks penalizing distant nodes (netrankr)
centrality_betweenness_network(): Betweenness centrality based on network flow (netrankr)
centrality_betweenness_current(): Betweenness centrality based on current flow (netrankr)
centrality_betweenness_communicability(): Betweenness centrality based on communicability (netrankr)
centrality_betweenness_rsp_simple(): Betweenness centrality based on simple randomised shortest path dependencies (netrankr)
centrality_betweenness_rsp_net(): Betweenness centrality based on net randomised shortest path dependencies (netrankr)
centrality_information(): centrality based on inverse sum of resistance distance between nodes (netrankr)
centrality_decay(): based on a power transformation of the shortest path (netrankr)
centrality_random_walk(): centrality based on the inverse sum of expected random walk length between nodes (netrankr)
centrality_expected(): Expected centrality ranking based on exact rank probability (netrankr)

Examples

create_notable('bull') %>%
  activate(nodes) %>%
  mutate(importance = centrality_alpha())
#> # A tbl_graph: 5 nodes and 5 edges
#> #
#> # An undirected simple graph with 1 component
#> #
#> # Node Data: 5 × 1 (active)
#>   importance
#>        <dbl>
#> 1         -1
#> 2         -1
#> 3         -1
#> 4          0
#> 5          0
#> #
#> # Edge Data: 5 × 2
#>    from    to
#>   <int> <int>
#> 1     1     2
#> 2     1     3
#> 3     2     3
#> # ℹ 2 more rows

# Most centrality measures are for nodes but not all
create_notable('bull') %>%
  activate(edges) %>%
  mutate(importance = centrality_edge_betweenness())
#> # A tbl_graph: 5 nodes and 5 edges
#> #
#> # An undirected simple graph with 1 component
#> #
#> # Edge Data: 5 × 3 (active)
#>    from    to importance
#>   <int> <int>      <dbl>
#> 1     1     2          2
#> 2     1     3          2
#> 3     2     3          4
#> 4     2     4          4
#> 5     3     5          4
#> #
#> # Node Data: 5 × 0