This function calculates the collective influence of input vertices and works with both directed and undirected networks. This function and its descriptions are obtained from https://github.com/ronammar/collective_influence with minor modifications. Collective Influence as described by Morone & Makse (2015). In simple terms, it is the product of the reduced degree (degree - 1) of a node and the total (sum of) reduced degrees of all nodes at a distance d from the node.

```
collective.influence(
graph,
vertices = V(graph),
mode = "all",
d = 3,
verbose = FALSE
)
```

- graph
A graph (network) of the igraph class.

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

- mode
The mode of collective influence depending on the directedness of the graph. If the graph is undirected, the mode "all" should be specified. Otherwise, for the calculation of collective influence 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".

- d
The distance, expressed in number of steps from a given node (default=3). Distance must be > 0. According to Morone & Makse (https://doi.org/10.1038/nature14604), 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.

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

A vector of collective influence for each vertex of the graph corresponding to the order of vertices output by V(graph).

Other centrality functions:
`betweenness()`

,
`clusterRank()`

,
`h_index()`

,
`lh_index()`

,
`neighborhood.connectivity()`

,
`sirir()`

```
if (FALSE) {
MyData <- coexpression.data
My_graph <- graph_from_data_frame(MyData)
GraphVertices <- V(My_graph)
ci <- collective.influence(graph = My_graph, vertices = GraphVertices, mode = "all", d=3)
}
```