This function calculates the IVI of the desired nodes from a graph. #' A shiny app has also been developed for the calculation of IVI as well as IVI-based network visualization, which is accessible using the `influential::runShinyApp("IVI")` command. You can also access the shiny app online at

  vertices = V(graph),
  weights = NULL,
  directed = FALSE,
  mode = "all",
  loops = TRUE,
  d = 3,
  scale = "range",
  ncores = "default",
  verbose = FALSE



A graph (network) of the igraph class.


A vector of desired vertices, which could be obtained by the V function.


Optional positive weight vector for calculating weighted betweenness centrality of nodes as a requirement for calculation of IVI. If the graph has a weight edge attribute, then this is used by default. Weights are used to calculate weighted shortest paths, so they are interpreted as distances.


Logical scalar, whether to directed graph is analyzed. This argument is ignored for undirected graphs.


The mode of IVI depending on the directedness of the graph. If the graph is undirected, the mode "all" should be specified. Otherwise, for the calculation of IVI based on incoming connections select "in" and for the outgoing connections select "out". Also, if all of the connections are desired, specify the "all" mode. Default mode is set to "all".


Logical; whether the loop edges are also counted.


The distance, expressed in number of steps from a given node (default=3). Distance must be > 0. According to Morone & Makse (, optimal results can be reached at d=3,4, but this depends on the size/"radius" of the network. NOTE: the distance d is not inclusive. This means that nodes at a distance of 3 from our node-of-interest do not include nodes at distances 1 and 2. Only 3.


Character string; the method used for scaling/normalizing the results. Options include 'range' (normalization within a 1-100 range), 'z-scale' (standardization using the z-score), and 'none' (no data scaling). The default selection is 'range'. Opting for the 'range' method is suitable when exploring a single network, allowing you to observe the complete spectrum and distribution of node influences. In this case, there is no intention to establish a specific threshold for the outcomes. However, it is possible to identify and present the top influential nodes based on their rankings. Conversely, the 'z-scale' option proves advantageous if the aim is to compare node influences across multiple networks or if there is a desire to establish a threshold (usually z-score > 1.645) for generating a list of the most influential nodes without manual intervention.


Integer; the number of cores to be used for parallel processing. If ncores == "default" (default), the number of cores to be used will be the max(number of available cores) - 1. We recommend leaving ncores argument as is (ncores = "default").


Logical; whether the accomplishment of different stages of the algorithm should be printed (default is FALSE).


A numeric vector with the IVI values based on the provided centrality measures.

See also


Other integrative ranking functions: comp_manipulate(), exir(), hubness.score(), ivi.from.indices(), spreading.score()


if (FALSE) {
MyData <-
My_graph <- graph_from_data_frame(MyData)
GraphVertices <- V(My_graph)
My.vertices.IVI <- ivi(graph = My_graph, vertices = GraphVertices,
                       weights = NULL, directed = FALSE, mode = "all",
                       loops = TRUE, d = 3, scale = "range")