`CINNA`

is an R package submitted on CRAN repository which has been written for centrality analysis in network science. It can be useful for assembling, comparing, evaluating and visualizing several types of centrality measures. This document is an introduction to the usage of this package and includes some user interface examples.

Centrality is defined as a measure for identifying the most important vertices within a network in graph theory. Several centrality types have been provided to compute central nodes by different formulas, while some analysis are needed to evaluate the most informative ones. In this package, we have prepared these resolutions and some examples of real networks.

For the examples in the following sections, we assume that the `CINNA`

package has been properly installed into the R environment. This can be done by typing

install.packages("CINNA")

into the R console. The `igraph`

[@Csardi2006] ,`network`

[@Butts2015;@Butts2008],`sna`

[@ButtsCT2008;@Butts2007] and `centiserve`

[@Jalili2015] packages are required and must be installed in your R environment as well. These are analogous to installing `CINNA`

and for more other calculations, packages such as `FactoMineR`

[@Sebastien2008], `plyr`

[@Wickham2011] `qdapTools`

[@Rinker2015], `Rtsne`

[@Krijthe2015] are necessary. For some plots, `factoextra`

[@Kassambara2015], `GGally`

[@Barret2016], `pheatmap`

[@kolde2015], `corrplot`

[@Taiyun2016], `dendextend`

[@Galili2015], `circlize`

[@Gu2014], `viridis`

[@Garnier2017] and `ggplot2`

[@Wickham2016] packages must be installed too. After installations, the `CINNA`

package can be loaded via

```
library(CINNA)
```

We collected five graphs instances based on factual datasets and natural networks. In order to develop some instructions for using this package, we prepared you a brief introduction about the topological of these networks as is described below:

| Name | Type | Description | Nodes | Edges | References | |:----------:|:----------------------:|:------------------------------------------------:|:-----:|:------:|:---------------:| | zachary | unweighted, undirected | friendships between members of a club | 34 | 78 | [@Zachary1977] | | cortex | unweighted, directed | pathways among cortical region in Macaque | 30 | 311 | [@Felleman1991] | | kangaroo | weighted, undirected | interactions between kangaroos | 17 | 90 | [@Kangaroo2016] | | rhesus | weighted, directed | grooming occurred among monkeys of an area | 16 | 110 | [@Rhesus2016] | | drugTarget | bipartite,directed |interactions among drugs and their protein targets| 1599 | 3766 | [@Barneh2015] |

`zachary`

[@Zachary1977] is an example of undirected and unweighted network in this package. This data set illustrates friendships between members of a university karate club. It is based on a faction membership after a social portion. The summary of important properties of this network is described below:

Edge Type: Friendship

Node Type: Person

Avg Edges: 77.50

Avg Nodes: 34.00

Graph properties: Unweighted, Undirected

This data set can be easily accessed by using data() function:

data("zachary") zachary

The result would have a class of "igraph" object.

`kangaroo`

[@Kangaroo2016] is a sample of undirected and weighted network which indicates interactions among free-ranging grey kangaroos. The edge between two nodes shows a dominance interaction between two kangaroos. The positive weight of each edge represents number of interaction between them. A brief explanation of it's properties is clarified below:

Edge Type: Interaction

Node Type: Kangaroo

Avg Edges: 91

Nodes: 17

Graph properties: Weighted, Undirected

Edge weights: Positive weights

`cortex`

[@Felleman1991] is a sample of macaque visual cortex network which is collected in 1991. In this data set, vertices represents neocortical areas which involved in visual functions in Macaques. The direction displays the progress of synapses from one to another. A summary of this can be as follows:

Edge Type: Pathway

Node Type: Cortical region

Avg Edges: 315.50

Nodes: 31.00

Graph properties: Directed, Unweighted

Edge weights: Positive weights

`rhesus`

[@Rhesus2016] is a directed and weighted network which describes grooming between free ranging rhesus macaques (Macaca mulatta) in Cayo Santiago during a two month period in 1963. In this data set a vertex is identified as a monkey and the directed edge among them means grooming between them. The weights of the edges demonstrates how often this manner happened. The network summary is as follows:

Edge Type: Grooming

Node Type: Monkey

Avg Edges: 111

Nodes: 16

Graph properties: Directed, Weighted

Edge weights: Positive weights

`drugTarget`

[@Barneh2015] is a bipartite, unconnected and directed network demonstrating interactions among Food and Drug Administration (FDA)-approved drugs and their corresponding protein targets. This network is a shrunken one in which metabolizing enzymes, carriers and transporters associated with drug metabolism are filtered and solely targets directly related to their pharmacological effects are included. A summary of this can be like:

Edge Type: interaction

Node Type: drug, protein target

Avg Edges: 3766

Nodes: 1599

Graph properties: Bipartite, unconnected, directed

In order to apply several centrality analysis, it is recommended to have a connected graph. Therefore, approaching the connected components of a network is needed. In order to extract components of a graph and use them for centrality analysis, we prepared some functions as below.

"graph.extract.components" function is able to read `igraph`

and `network`

objects and returns their components as a list of `igraph`

objects. This function also has this ability to recognized bipartite graphs and user can decide that which project is suitable for his analysis. In order to use this function, we use zachary data set and develop it in all of our functions.

```
graph_extract_components(zachary)
```

This results the only component of the zachary graph. This function is also applicable for bipartite networks. Using the `num_proj`

argument, user can decide on which projection is interested to work on. As an example of bipartite graphs, we use `drugTarget`

network as follows:

data("drugTarget") drug_comp <- graph_extract_components( drugTarget, directed = TRUE, bipartite_proj = TRUE, num_proj = 1) head(drug_comp)

It will return all components of the second projection of the network.

If you had an edge list, an adjacency matrix or a grapnel format of a network, the `misc_extract_components`

can be useful. This function extracts the components of other formats of graph. For illustration, we convert `zachary`

graph to an edge list to be able to use it for this function.

library(igraph) zachary_edgelist <- as_edgelist(zachary) misc_extract_components(zachary_edgelist)

In the most of research topics of network analysis, network features are related to the largest connected component of a graph[@Newman2010]. In order to get that for an `igraph`

or a `network`

object, `giant_component_extract`

function is specified. For using this function we can do:

```
giant_component_extract(zachary)
```

This function extracts the strongest components of the input network as `igraph`

objects.

This section particularly is specified for centrality analysis in network science.

All of the introduced centrality measures are not appropriate for all types of networks. So, to figure out which of them is suitable, `proper_centralities`

is specified. This function distinguishes proper centrality types based on network topology. To use this, we can do:

```
proper_centralities(zachary)
```

It returns the full names of suitable centrality types for the input graph. The input must have a class of `igraph`

object.

In the next step, proper centralities and those which are looking for can be chosen. In order to compute proper centrality types resulted from the `proper_centralities`

, you can use `calculate_centralities`

function as below.

calculate_centralities(zachary, include = "Degree Centrality")

In this function, you have the ability to specify some centrality types that is not your favor to calculate by the `conclude`

argument. Here, we will select first ten centrality measures for an illustration:

pr_cent <- proper_centralities(zachary) calc_cent <- calculate_centralities(zachary, include = pr_cent[1:10])

The result would be a list of computed centralities.

In order to figure out the order of most important centrality types based on your graph structure, `pca_centralities`

function can be used. This applies principal component analysis on the computed centrality values[@Husson2010]. For this, the result of `calculate_centralities`

method is needed:

```
pca_centralities( calc_cent )
```

For choosing the number of principal components, we considered cumulative percentage of variance values which are more than 80 as the cut off which can be edited using `cut.off`

argument. It returns a plot for visualizing contribution values of the computed centrality measures due to the number of principal components. The `scale.unit`

argument gives the ability to whether it should normalize the input or not.

pca_centralities( calc_cent , scale.unit = FALSE )

Another method for distinguishing which centrality measure has more information or in another words has more costs is using (t-SNE) t-Distributed Stochastic Neighbor Embedding analysis[@VanDerMaaten2014]. This is a non-linear dimensional reduction algorithm used for high-dimensional data. `tsne_centralities`

function applies t-sne on centrality measure values like below:

tsne_centralities( calc_cent, dims = 2, perplexity = 1, scale=TRUE)

This returns the bar plot of computed cost values of each centrality measure on a plot. In order to access only computed values of PCA and t-sne methods, `summary_pca_centralities`

and `tsne_centralities`

functions can be helpful.

To visualize the results of network centrality analysis some convenient functions have been developed as it described below.

After evaluating centrality measures, demonstrating high values of centralities in some nodes gives an overall insight about the network to the researcher. By using `visualize_graph`

function, you will be able to illustrate the input graph based on the specified centrality value. If the centrality measure values were computed, `computed.centrality.value`

argument is recommended. Otherwise, using `centrality.type`

argument, the function will compute centrality based on the input name of centrality type. For practice, we specifies `Degree Centrality`

. Here,

visualize_graph( zachary , centrality.type="Degree Centrality")

On of the way of complex large network visualizations(more than 100 nodes and 200 edges) is using heat map[@Pryke2007].
`visualize_heatmap`

function demonstrates a heat map plot between the centrality values. The input is a list containing the computed values.

visualize_heatmap( calc_cent , scale = TRUE )

Comprehending pair correlation among centralities is a popular analysis for researchers[@Dwyer2006]. In order to that, `visualize_correlations`

method is appropriate. In this you are able to specify the type of correlation which you are enthusiastic to obtain.

visualize_correlations(calc_cent,"pearson")

In order to visualize a simple clustering across the nodes of a graph based on a specific centrality measure, we can use the `visualize_dendrogram`

function. This function draw a dendrogram plot in which colors indicate the clusters.

visualize_dendrogram(zachary, k=4)

In this package additionally to correlation calculation, ability to apply linear regression for each pair of centralities has been prepared to realize the association between centralities. For visualization, `visualize_association`

method is an appropriate function to use:

subgraph_cent <- calc_cent[[1]] Topological_coef <- calc_cent[[2]] visualize_association( subgraph_cent , Topological_coef)

To access the distribution of centrality values and their corresponding pair correlation value, `visualize_pair_correlation`

would be helpful. The Pearson correlation[@Benesty2009] has been used for this method.

```
visualize_pair_correlation( subgraph_cent , Topological_coef)
```

The result is a scatter plot visualizing correlation values.

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