centrality function

Calculate node and edge centrality

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

Returns

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())

# Most centrality measures are for nodes but not all
create_notable('bull') %>%
  activate(edges) %>%
  mutate(importance = centrality_edge_betweenness())