- 1 Overview
- 2 Fase correlation analysis
- 3 Network reconstruction
- 4 Calculation of centrality measures
- 5 Assessment of the association of centrality measures
- 6 Identification of the most
`influential`

network nodes - 7 Identification of the most important network spreaders
- 8 Identification of the most important network hubs
- 9 Ranking the influence of nodes on
the topology of a network based on the
`SIRIR`

model - 10 Experimental data-based classification and ranking of top candidate features
- 11 Computational manipulation of cells
- 12 References

`influential`

is an R package mainly for the
identification of the most influential nodes in a network as well as the
classification and ranking of top candidate features. The
`influential`

package contains several functions that could
be categorized into five groups according to their purpose:

- Network reconstruction
- Calculation of centrality measures
- Assessment of the association of centrality measures
- Identification of the most
`influential`

network nodes - Experimental data-based classification and ranking of features

The sections below introduce these five categories. However, if you
wish not going through all of the functions and their applications, you
may skip to any of the novel methods proposed by the
`influential`

, including:

Correlation (association/similarity/dissimilarity) analysis is the
first required step before network reconstructions. Although R base
`cor`

function makes it possible to perform correlation
analysis of a table, this function is notably slow in the correlation
analysis of large datasets. Also, calculation of probability values is
not possible for all correlations between all pairs of features
simultaneously. The `fcor`

function calculates
Pearson/Spearman correlations between all pairs of features in a
matrix/dataframe much faster than the base R cor function. It is also
possible to simultaneously calculate mutual rank (MR) of correlations as
well as their p-values and adjusted p-values. Additionally, this
function can automatically combine and flatten the result matrices.
Selecting correlated features using an MR-based threshold rather than
based on their correlation coefficients or an arbitrary p-value is more
efficient and accurate in inferring functional associations in systems,
for example in gene regulatory networks.

Here is an example of performing correlation analysis using the
`fcor`

function.

```
# Prepare a sample dataset
set.seed(60)
my_data <- matrix(data = runif(n = 10000, min = 2, max = 300),
nrow = 50, ncol = 200,
dimnames = list(c(paste("sample", c(1:50), sep = "_")),
c(paste("gene", c(1:200), sep = "_")))
)
```

Have a look at top 5 samples and gene (rows and columns) of the
`my_data`

:

gene_1 | gene_2 | gene_3 | gene_4 | gene_5 | |
---|---|---|---|---|---|

sample_1 | 229.80194 | 202.09477 | 286.98031 | 212.86299 | 255.15716 |

sample_2 | 107.12704 | 262.56776 | 92.47135 | 263.67454 | 188.00376 |

sample_3 | 208.04590 | 123.99512 | 284.35705 | 173.80360 | 270.60758 |

sample_4 | 209.36913 | 141.90713 | 154.59261 | 130.17074 | 219.54511 |

sample_5 | 86.21945 | 14.10478 | 258.05186 | 40.89961 | 18.83074 |

```
# Calculate correlations between all pairs of genes
correlation_tbl <- fcor(data = my_data,
method = "spearman",
mutualRank = TRUE,
pvalue = "TRUE", adjust = "BH",
flat = TRUE)
```

Now have a look at the top 10 rows of the
`correlation_tbl`

:

row | column | cor | mr | p | p.adj |
---|---|---|---|---|---|

gene_1 | gene_2 | 0.3373349 | 3.872983 | 0.0165899 | 0.8096184 |

gene_1 | gene_3 | 0.0721729 | 122.270193 | 0.6184265 | 0.9981266 |

gene_2 | gene_3 | 0.0002401 | 200.000000 | 0.9986797 | 0.9995793 |

gene_1 | gene_4 | -0.0636255 | 132.864593 | 0.6606863 | 0.9981266 |

gene_2 | gene_4 | 0.0124370 | 182.931681 | 0.9316877 | 0.9981266 |

gene_3 | gene_4 | -0.0945498 | 108.958708 | 0.5136765 | 0.9981266 |

gene_1 | gene_5 | -0.0616086 | 136.167177 | 0.6708188 | 0.9981266 |

gene_2 | gene_5 | -0.1063625 | 90.862533 | 0.4622400 | 0.9981266 |

gene_3 | gene_5 | 0.2174790 | 25.922963 | 0.1292321 | 0.9700054 |

gene_4 | gene_5 | 0.0341417 | 171.499271 | 0.8139135 | 0.9981266 |

Three functions have been obtained from the `igraph`

^{1} R package
for the reconstruction of networks.

In the data frame the first and second columns should be composed of
source and target nodes.

A sample appropriate data frame is brought below:

lncRNA | Coexpressed.Gene |
---|---|

ADAMTS9-AS2 | A2M |

ADAMTS9-AS2 | ABCA6 |

ADAMTS9-AS2 | ABCA8 |

ADAMTS9-AS2 | ABCA9 |

ADAMTS9-AS2 | ABI3BP |

ADAMTS9-AS2 | AC093110.3 |

This is a co-expression dataset obtained from a paper by Salavaty
**et al**.^{2}

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(d=MyData)
```

If you look at the class of `My_graph`

you should see that
it has an `igraph`

class:

A sample appropriate adjacency matrix is brought below:

LINC00891 | LINC00968 | LINC00987 | LINC01506 | MAFG-AS1 | MIR497HG | |
---|---|---|---|---|---|---|

LINC00891 | 0 | 1 | 1 | 0 | 0 | 0 |

LINC00968 | 0 | 0 | 1 | 0 | 0 | 0 |

LINC00987 | 0 | 1 | 0 | 0 | 0 | 0 |

LINC01506 | 0 | 0 | 0 | 0 | 0 | 0 |

MAFG-AS1 | 0 | 0 | 0 | 0 | 0 | 0 |

MIR497HG | 0 | 1 | 1 | 0 | 0 | 0 |

- Note that the matrix has the same number of rows and columns.

A sample appropriate incidence matrix is brought below:

Gene_1 | Gene_2 | Gene_3 | Gene_4 | Gene_5 | |
---|---|---|---|---|---|

cell_1 | 0 | 1 | 1 | 0 | 1 |

cell_2 | 1 | 1 | 1 | 0 | 0 |

cell_3 | 1 | 1 | 1 | 0 | 0 |

cell_4 | 0 | 0 | 0 | 1 | 0 |

To calculate the centrality of nodes within a network several
different options are available. The following sections describe how to
obtain the names of network nodes and use different functions to
calculate the centrality of nodes within a network. Although several
centrality functions are provided, we recommend the IVI for the identification of the most
`influential`

nodes within a network.

By the way, the results of all of the following centrality functions could be conveniently illustrated using the centrality-based network visualization function.

Network vertices (nodes) are required in order to calculate their
centrality measures. Thus, before calculation of network centrality
measures we need to obtain the name of required network vertices. To
this end, we use the `V`

function, which is obtained from the
`igraph`

package. However, you may provide a character vector
of the name of your desired nodes manually.

- Note in many of the centrality index functions the entire network nodes are assessed if no vector of desired vertices is provided.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
My_graph_vertices <- V(My_graph)
head(My_graph_vertices)
#> + 6/794 vertices, named, from 775cff6:
#> [1] ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
```

Degree centrality is the most commonly used local centrality measure
which could be calculated via the `degree`

function obtained
from the `igraph`

package.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculating degree centrality
My_graph_degree <- degree(My_graph, v = GraphVertices, normalized = FALSE)
head(My_graph_degree)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 172 121 168 26 189 176
```

Degree centrality could be also calculated for *directed*
graphs via specifying the `mode`

parameter.

Betweenness centrality, like degree centrality, is one of the most
commonly used centrality measures but is representative of the global
centrality of a node. This centrality metric could also be calculated
using a function obtained from the `igraph`

package.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculating betweenness centrality
My_graph_betweenness <- betweenness(My_graph, v = GraphVertices,
directed = FALSE, normalized = FALSE)
head(My_graph_betweenness)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 21719.857 28185.199 26946.625 2940.467 33333.369 21830.511
```

Betweenness centrality could be also calculated for *directed*
and/or *weighted* graphs via specifying the `directed`

and `weights`

parameters, respectively.

Neighborhood connectivity is one of the other important centrality
measures that reflect the semi-local centrality of a node. This
centrality measure was first represented in a Science paper^{3} in 2002
and is for the first time calculable in R environment via the
`influential`

package.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculating neighborhood connectivity
neighrhood.co <- neighborhood.connectivity(graph = My_graph,
vertices = GraphVertices,
mode = "all")
head(neighrhood.co)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 11.290698 4.983471 7.970238 3.000000 15.153439 13.465909
```

Neighborhood connectivity could be also calculated for
*directed* graphs via specifying the `mode`

parameter.

H-index is H-index is another semi-local centrality measure that was
inspired from its application in assessing the impact of researchers and
is for the first time calculable in R environment via the
`influential`

package.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculating H-index
h.index <- h_index(graph = My_graph,
vertices = GraphVertices,
mode = "all")
head(h.index)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 11 9 11 2 12 12
```

H-index could be also calculated for *directed* graphs via
specifying the `mode`

parameter.

Local H-index (LH-index) is a semi-local centrality measure and an
improved version of H-index centrality that leverages the H-index to the
second order neighbors of a node and is for the first time calculable in
R environment via the `influential`

package.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculating Local H-index
lh.index <- lh_index(graph = My_graph,
vertices = GraphVertices,
mode = "all")
head(lh.index)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 1165 446 994 34 1289 1265
```

Local H-index could be also calculated for *directed* graphs
via specifying the `mode`

parameter.

Collective Influence (CI) is a global centrality measure that calculates the product of the reduced degree (degree - 1) of a node and the total reduced degree of all nodes at a distance d from the node. This centrality measure is for the first time provided in an R package.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculating Collective Influence
ci <- collective.influence(graph = My_graph,
vertices = GraphVertices,
mode = "all", d=3)
head(ci)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 9918 70560 39078 675 10716 7350
```

Collective Influence could be also calculated for *directed*
graphs via specifying the `mode`

parameter.

ClusterRank is a local centrality measure that makes a connection between local and semi-local characteristics of a node and at the same time removes the negative effects of local clustering.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculating ClusterRank
cr <- clusterRank(graph = My_graph,
vids = GraphVertices,
directed = FALSE, loops = TRUE)
head(cr)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 63.459812 5.185675 21.111776 1.280000 135.098278 81.255195
```

ClusterRank could be also calculated for *directed* graphs via
specifying the `directed`

parameter.

The function `cond.prob.analysis`

assesses the conditional
probability of deviation of two centrality measures (or any other two
continuous variables) from their corresponding means in opposite
directions.

```
# Preparing the data
MyData <- centrality.measures
# Assessing the conditional probability
My.conditional.prob <- cond.prob.analysis(data = MyData,
nodes.colname = rownames(MyData),
Desired.colname = "BC",
Condition.colname = "NC")
print(My.conditional.prob)
#> $ConditionalProbability
#> [1] 51.61871
#>
#> $ConditionalProbability_split.half.sample
#> [1] 51.73611
```

- As you can see in the results, the whole data is also randomly splitted into half in order to further test the validity of conditional probability assessments.
*The higher the conditional probability the more two centrality measures behave in contrary manners*.

The function `double.cent.assess`

could be used to
automatically assess both the distribution mode of centrality measures
(two continuous variables) and the nature of their association. The
analyses done through this formula are as follows:

**Normality assessment**:- Variables with
**lower than**5000 observations:*Shapiro-Wilk test* - Variables with
**over**5000 observations:*Anderson-Darling test*

- Variables with
**Assessment of non-linear/non-monotonic correlation**:*Non-linearity assessment*: Fitting a generalized additive model (GAM) with integrated smoothness approximations using the`mgcv`

package*Non-monotonicity assessment*: Comparing the squared coefficients of the correlation based on Spearman’s rank correlation analysis and ranked regression test with non-linear splines.- Squared coefficient of Spearman’s rank correlation
**>**R-squared ranked regression with non-linear splines:*Monotonic* - Squared coefficient of Spearman’s rank correlation
**<**R-squared ranked regression with non-linear splines:*Non-monotonic*

- Squared coefficient of Spearman’s rank correlation

**Dependence assessment**:*Hoeffding’s independence test*: Hoeffding’s test of independence is a test based on the population measure of deviation from independence which computes a D Statistics ranging from -0.5 to 1: Greater D values indicate a higher dependence between variables.*Descriptive non-linear non-parametric dependence test*: This assessment is based on non-linear non-parametric statistics (NNS) which outputs a dependence value ranging from 0 to 1. For further details please refer to the NNS R package^{4}: Greater values indicate a higher dependence between variables.

**Correlation assessment**: As the correlation between most of the centrality measures follows a non-monotonic form, this part of the assessment is done based on the NNS statistics which itself calculates the correlation based on partial moments and outputs a correlation value ranging from -1 to 1. For further details please refer to the NNS R package.**Assessment of conditional probability of deviation from means**This step assesses the conditional probability of deviation of two centrality measures (or any other two continuous variables) from their corresponding means in opposite directions.- The independent centrality measure (variable) is considered as the condition variable and the other as the desired one.
- As you will see in the results, the whole data is also randomly splitted into half in order to further test the validity of conditional probability assessments.
*The higher the conditional probability the more two centrality measures behave in contrary manners*.

```
# Preparing the data
MyData <- centrality.measures
# Association assessment
My.metrics.assessment <- double.cent.assess(data = MyData,
nodes.colname = rownames(MyData),
dependent.colname = "BC",
independent.colname = "NC")
print(My.metrics.assessment)
#> $Summary_statistics
#> BC NC
#> Min. 0.000000000 1.2000
#> 1st Qu. 0.000000000 66.0000
#> Median 0.000000000 156.0000
#> Mean 0.005813357 132.3443
#> 3rd Qu. 0.000340000 179.3214
#> Max. 0.529464720 192.0000
#>
#> $Normality_results
#> p.value
#> BC 1.415450e-50
#> NC 9.411737e-30
#>
#> $Dependent_Normality
#> [1] "Non-normally distributed"
#>
#> $Independent_Normality
#> [1] "Non-normally distributed"
#>
#> $GAM_nonlinear.nonmonotonic.results
#> edf p-value
#> 8.992406 0.000000
#>
#> $Association_type
#> [1] "nonlinear-nonmonotonic"
#>
#> $HoeffdingD_Statistic
#> D_statistic P_value
#> Results 0.01770279 1e-08
#>
#> $Dependence_Significance
#> Hoeffding
#> Results Significantly dependent
#>
#> $NNS_dep_results
#> Correlation Dependence
#> Results -0.7948106 0.8647164
#>
#> $ConditionalProbability
#> [1] 55.35386
#>
#> $ConditionalProbability_split.half.sample
#> [1] 55.90331
```

**Note**: It should also be noted that as a single
regression line does not fit all models with a certain degree of
freedom, based on the size and correlation mode of the variables
provided, this function might return an error due to incapability of
running step 2. In this case, you may follow each step manually or as an
alternative run the other function named
`double.cent.assess.noRegression`

which does not perform any
regression test and consequently it is not required to determine the
dependent and independent variables.

The function `double.cent.assess.noRegression`

could be
used to automatically assess both the distribution mode of centrality
measures (two continuous variables) and the nature of their association.
The analyses done through this formula are as follows:

**Normality assessment**:- Variables with
**lower than**5000 observations:*Shapiro-Wilk test* - Variables with
**over**5000 observations:*Anderson–Darling test*

- Variables with
**Dependence assessment**:*Hoeffding’s independence test*: Hoeffding’s test of independence is a test based on the population measure of deviation from independence which computes a D Statistics ranging from -0.5 to 1: Greater D values indicate a higher dependence between variables.*Descriptive non-linear non-parametric dependence test*: This assessment is based on non-linear non-parametric statistics (NNS) which outputs a dependence value ranging from 0 to 1. For further details please refer to the NNS R package: Greater values indicate a higher dependence between variables.

**Correlation assessment**: As the correlation between most of the centrality measures follows a non-monotonic form, this part of the assessment is done based on the NNS statistics which itself calculates the correlation based on partial moments and outputs a correlation value ranging from -1 to 1. For further details please refer to the NNS R package.**Assessment of conditional probability of deviation from means**This step assesses the conditional probability of deviation of two centrality measures (or any other two continuous variables) from their corresponding means in opposite directions.- The
`centrality2`

variable is considered as the condition variable and the other (`centrality1`

) as the desired one. - As you will see in the results, the whole data is also randomly splitted into half in order to further test the validity of conditional probability assessments.
*The higher the conditional probability the more two centrality measures behave in contrary manners*.

- The

```
# Preparing the data
MyData <- centrality.measures
# Association assessment
My.metrics.assessment <- double.cent.assess.noRegression(data = MyData,
nodes.colname = rownames(MyData),
centrality1.colname = "BC",
centrality2.colname = "NC")
print(My.metrics.assessment)
#> $Summary_statistics
#> BC NC
#> Min. 0.000000000 1.2000
#> 1st Qu. 0.000000000 66.0000
#> Median 0.000000000 156.0000
#> Mean 0.005813357 132.3443
#> 3rd Qu. 0.000340000 179.3214
#> Max. 0.529464720 192.0000
#>
#> $Normality_results
#> p.value
#> BC 1.415450e-50
#> NC 9.411737e-30
#>
#> $Centrality1_Normality
#> [1] "Non-normally distributed"
#>
#> $Centrality2_Normality
#> [1] "Non-normally distributed"
#>
#> $HoeffdingD_Statistic
#> D_statistic P_value
#> Results 0.01770279 1e-08
#>
#> $Dependence_Significance
#> Hoeffding
#> Results Significantly dependent
#>
#> $NNS_dep_results
#> Correlation Dependence
#> Results -0.7948106 0.8647164
#>
#> $ConditionalProbability
#> [1] 55.35386
#>
#> $ConditionalProbability_split.half.sample
#> [1] 55.68163
```

`influential`

network nodes**IVI** : `IVI`

is the first integrative
method for the identification of network most influential nodes in a way
that captures all network topological dimensions. The `IVI`

formula integrates the most important local (i.e. degree centrality and
ClusterRank), semi-local (i.e. neighborhood connectivity and local
H-index) and global (i.e. betweenness centrality and collective
influence) centrality measures in such a way that both synergizes their
effects and removes their biases.

```
# Preparing the data
MyData <- centrality.measures
# Calculation of IVI
My.vertices.IVI <- ivi.from.indices(DC = MyData$DC,
CR = MyData$CR,
NC = MyData$NC,
LH_index = MyData$LH_index,
BC = MyData$BC,
CI = MyData$CI)
head(My.vertices.IVI)
#> [1] 24.670056 8.344337 18.621049 1.017768 29.437028 33.512598
```

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculation of IVI
My.vertices.IVI <- ivi(graph = My_graph, vertices = GraphVertices,
weights = NULL, directed = FALSE, mode = "all",
loops = TRUE, d = 3, scale = "range")
head(My.vertices.IVI)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 39.53878 19.94999 38.20524 1.12371 100.00000 47.49356
```

IVI could be also calculated for *directed* and/or
*weighted* graphs via specifying the `directed`

,
`mode`

, and `weights`

parameters.

Check out our
paper^{5} for a more complete description of the IVI
formula and all of its underpinning methods and analyses.

The following tutorial video demonstrates how to simply calculate the IVI value of all of the nodes within a network.

The `cent_network.vis`

is a function for the visualization
of a network based on applying a centrality measure to the size and
color of network nodes. The centrality of network nodes could be
calculated by any means and based on any centrality index. Here, we
demonstrate the visualization of a network according to IVI values.

```
# Reconstructing the graph
set.seed(70)
My_graph <- igraph::sample_gnm(n = 50, m = 120, directed = TRUE)
# Calculating the IVI values
My_graph_IVI <- ivi(My_graph, directed = TRUE)
# Visualizing the graph based on IVI values
My_graph_IVI_Vis <- cent_network.vis(graph = My_graph,
cent.metric = My_graph_IVI,
directed = TRUE,
plot.title = "IVI-based Network",
legend.title = "IVI value")
My_graph_IVI_Vis
```

The above figure illustrates a simple use case of the function
`cent_network.vis`

. You can apply this function to
directed/undirected and/or weighted/unweighted networks. Also, a
complete flexibility (list of arguments) have been provided for the
adjustment of colors, transparencies, sizes, titles, etc. Additionally,
several different layouts have been provided that could be conveniently
applied to a network.

In the case of highly crowded networks, the “

grid” layout would be most appropriate.

The following tutorial video demonstrates how to visualize a network
based on the centrality of nodes (e.g. their `IVI`

values).

A shiny app has also been developed for the calculation of IVI as
well as IVI-based network visualization, which is accessible using the
following command.

`influential::runShinyApp("IVI")`

You can also access the shiny app online at the Influential Software Package
server.

Sometimes we seek to identify not necessarily the most influential nodes but the nodes with most potential in spreading of information throughout the network.

**Spreading score** : `spreading.score`

is an
integrative score made up of four different centrality measures
including ClusterRank, neighborhood connectivity, betweenness
centrality, and collective influence. Also, Spreading score reflects the
spreading potential of each node within a network and is one of the
major components of the `IVI`

.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculation of Spreading score
Spreading.score <- spreading.score(graph = My_graph,
vertices = GraphVertices,
weights = NULL, directed = FALSE, mode = "all",
loops = TRUE, d = 3, scale = "range")
head(Spreading.score)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 42.932497 38.094111 45.114648 1.587262 100.000000 49.193292
```

Spreading score could be also calculated for *directed* and/or
*weighted* graphs via specifying the `directed`

,
`mode`

, and `weights`

parameters. The results
could be conveniently illustrated using the centrality-based network visualization function.

In some cases we want to identify not the nodes with the most sovereignty in their surrounding local environments.

**Hubness score** : `hubness.score`

is an
integrative score made up of two different centrality measures including
degree centrality and local H-index. Also, Hubness score reflects the
power of each node in its surrounding environment and is one of the
major components of the `IVI`

.

```
# Preparing the data
MyData <- coexpression.data
# Reconstructing the graph
My_graph <- graph_from_data_frame(MyData)
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculation of Hubness score
Hubness.score <- hubness.score(graph = My_graph,
vertices = GraphVertices,
directed = FALSE, mode = "all",
loops = TRUE, scale = "range")
head(Hubness.score)
#> ADAMTS9-AS2 C8orf34-AS1 CADM3-AS1 FAM83A-AS1 FENDRR LANCL1-AS1
#> 84.299719 46.741660 77.441514 8.437142 92.870451 88.734131
```

Spreading score could be also calculated for *directed* graphs
via specifying the `directed`

and `mode`

parameters. The results could be conveniently illustrated using the centrality-based network visualization function.

`SIRIR`

model**SIRIR** : `SIRIR`

is achieved by the
integration of susceptible-infected-recovered (SIR) model with the
leave-one-out cross validation technique and ranks network nodes based
on their true universal influence on the network topology and spread of
information. One of the applications of this function is the assessment
of performance of a novel algorithm in identification of network
influential nodes.

```
# Reconstructing the graph
My_graph <- sif2igraph(Path = "Sample_SIF.sif")
# Extracting the vertices
GraphVertices <- V(My_graph)
# Calculation of influence rank
Influence.Ranks <- sirir(graph = My_graph,
vertices = GraphVertices,
beta = 0.5, gamma = 1, no.sim = 10, seed = 1234)
```

difference.value | rank | |
---|---|---|

MRAP | 49.7 | 1 |

FOXM1 | 49.5 | 2 |

ATAD2 | 49.5 | 2 |

POSTN | 49.4 | 4 |

CDC7 | 49.3 | 5 |

ZWINT | 42.1 | 6 |

MKI67 | 41.9 | 7 |

FN1 | 41.9 | 7 |

ASPM | 41.8 | 9 |

ANLN | 41.8 | 9 |

**ExIR** : `ExIR`

is a model for the
classification and ranking of top candidate features. The input data
could come from any type of experiment such as transcriptomics and
proteomics. This model is based on multi-level filtration and scoring
based on several supervised and unsupervised analyses followed by the
classification and integrative ranking of top candidate features. Using
this function and depending on the input data and specified arguments,
the user can get a graph object and one to four tables including:

**Drivers**: Prioritized drivers are supposed to have the highest impact on the progression of a biological process or disease under investigation.**Biomarkers**: Prioritized biomarkers are supposed to have the highest sensitivity to different conditions under investigation and the severity of each condition.**DE-mediators**: Prioritized DE-mediators are those features that are differentially expressed/abundant but in a fluctuating manner and play mediatory roles between drivers.**nonDE-mediators**: Prioritized nonDE-mediators are those features that are not differentially expressed/abundant but have associations with and play mediatory roles between drivers.

First, prepare your data. Suppose we have the data for time-course transcriptomics and we have previously performed differential expression analysis for each step-wise pair of time-points. Also, we have performed trajectory analysis to identify the genes that have significant alterations across all time-points.

```
# Prepare sample data
gene.names <- paste("gene", c(1:2000), sep = "_")
set.seed(60)
tp2.vs.tp1.DEGs <- data.frame(logFC = rnorm(n = 700, mean = 2, sd = 4),
FDR = runif(n = 700, min = 0.0001, max = 0.049))
set.seed(60)
rownames(tp2.vs.tp1.DEGs) <- sample(gene.names, size = 700)
set.seed(70)
tp3.vs.tp2.DEGs <- data.frame(logFC = rnorm(n = 1300, mean = -1, sd = 5),
FDR = runif(n = 1300, min = 0.0011, max = 0.039))
set.seed(70)
rownames(tp3.vs.tp2.DEGs) <- sample(gene.names, size = 1300)
set.seed(80)
regression.data <- data.frame(R_squared = runif(n = 800, min = 0.1, max = 0.85))
set.seed(80)
rownames(regression.data) <- sample(gene.names, size = 800)
```

Use the function `diff_data.assembly`

to automatically
generate the Diff_data table for the `ExIR`

model.

```
my_Diff_data <- diff_data.assembly(tp2.vs.tp1.DEGs,
tp3.vs.tp2.DEGs,
regression.data)
my_Diff_data[c(1:10),]
```

Have a look at the top 10 rows of the `Diff_data`

data
frame:

Diff_value1 | Sig_value1 | Diff_value2 | Sig_value2 | Diff_value3 | |
---|---|---|---|---|---|

gene_17331 | 4.9 | 0 | 0 | 1 | 0 |

gene_12546 | 4.0 | 0 | 0 | 1 | 0 |

gene_12837 | -0.3 | 0 | 0 | 1 | 0 |

gene_18522 | 1.4 | 0 | 0 | 1 | 0 |

gene_6260 | -4.9 | 0 | 0 | 1 | 0 |

gene_2722 | -4.9 | 0 | 0 | 1 | 0 |

gene_19882 | 6.3 | 0 | 0 | 1 | 0 |

gene_2790 | 3.3 | 0 | 0 | 1 | 0 |

gene_17011 | -1.6 | 0 | 0 | 1 | 0 |

gene_8321 | 3.8 | 0 | 0 | 1 | 0 |

Now, prepare a sample normalized experimental data matrix

```
set.seed(60)
MyExptl_data <- matrix(data = runif(n = 100000, min = 2, max = 300),
nrow = 50, ncol = 2000,
dimnames = list(c(paste("cancer_sample", c(1:25), sep = "_"),
paste("normal_sample", c(1:25), sep = "_")),
gene.names))
# Log transform the data to bring them closer to normal distribution
MyExptl_data <- log2(MyExptl_data)
MyExptl_data[c(1:5, 45:50),c(1:5)]
```

Have a look at top 5 cancer and normal samples (rows) of the
`Exptl_data`

:

gene_1 | gene_2 | gene_3 | gene_4 | gene_5 | |
---|---|---|---|---|---|

cancer_sample_1 | 8 | 8 | 8 | 8 | 8 |

cancer_sample_2 | 7 | 8 | 6 | 8 | 8 |

cancer_sample_3 | 8 | 7 | 8 | 7 | 8 |

cancer_sample_4 | 8 | 7 | 7 | 7 | 8 |

cancer_sample_5 | 6 | 4 | 8 | 5 | 4 |

normal_sample_20 | 8 | 7 | 7 | 8 | 8 |

normal_sample_21 | 8 | 7 | 8 | 6 | 8 |

normal_sample_22 | 8 | 8 | 8 | 7 | 6 |

normal_sample_23 | 7 | 6 | 8 | 7 | 8 |

normal_sample_24 | 8 | 8 | 7 | 5 | 7 |

normal_sample_25 | 5 | 7 | 8 | 8 | 6 |

Now add the “condition” column to the Exptl_data table.

`ExIR`

modelFinally, prepare the other required input data for the
`ExIR`

model.

```
#The table of differential/regression previously prepared
my_Diff_data
#The column indices of differential values in the Diff_data table
Diff_value <- c(1,3)
#The column indices of regression values in the Diff_data table
Regr_value <- 5
#The column indices of significance (P-value/FDR) values in
# the Diff_data table
Sig_value <- c(2,4)
#The matrix/data frame of normalized experimental
# data previously prepared
MyExptl_data
#The name of the column delineating the conditions of
# samples in the Exptl_data matrix
Condition_colname <- "condition"
#The desired list of features
set.seed(60)
MyDesired_list <- sample(gene.names, size = 500) #Optional
#Running the ExIR model
My.exir <- exir(Desired_list = MyDesired_list,
cor_thresh_method = "mr", mr = 100,
Diff_data = my_Diff_data, Diff_value = Diff_value,
Regr_value = Regr_value, Sig_value = Sig_value,
Exptl_data = MyExptl_data, Condition_colname = Condition_colname,
seed = 60, verbose = FALSE)
names(My.exir)
#> [1] "Driver table" "DE-mediator table" "Biomarker table" "Graph"
class(My.exir)
#> [1] "ExIR_Result"
```

Have a look at the heads of the output tables of ExIR:

**Drivers**

Score | Z.score | Rank | P.value | P.adj | Type | |
---|---|---|---|---|---|---|

gene_947 | 5.774833 | -0.9620144 | 286 | 0.8319788 | 0.8817412 | Accelerator |

gene_90 | 35.813378 | 0.9440501 | 54 | 0.1725720 | 0.8817412 | Decelerator |

gene_116 | 11.060591 | -0.6266121 | 221 | 0.7345432 | 0.8817412 | Decelerator |

gene_96 | 8.687675 | -0.7771830 | 248 | 0.7814746 | 0.8817412 | Accelerator |

gene_674 | 28.826453 | 0.5007021 | 77 | 0.3082904 | 0.8817412 | Decelerator |

gene_1017 | 24.162479 | 0.2047545 | 100 | 0.4188820 | 0.8817412 | Accelerator |

**Biomarkers**

Score | Z.score | Rank | P.value | P.adj | Type | |
---|---|---|---|---|---|---|

gene_947 | 1.000003 | -0.2050551 | 269 | 0.58123546 | 0.5812356 | Up-regulated |

gene_90 | 1.000007 | -0.2050545 | 246 | 0.58123524 | 0.5812356 | Down-regulated |

gene_116 | 1.000002 | -0.2050552 | 276 | 0.58123549 | 0.5812356 | Down-regulated |

gene_96 | 1.308484 | -0.1644440 | 70 | 0.56530917 | 0.5812356 | Up-regulated |

gene_674 | 1.017092 | -0.2028053 | 125 | 0.58035641 | 0.5812356 | Down-regulated |

gene_1017 | 12.507207 | 1.3098553 | 12 | 0.09512239 | 0.5812356 | Up-regulated |

**DE-mediators**

Score | Z.score | Rank | P.value | P.adj | |
---|---|---|---|---|---|

gene_592 | 11.10698 | -1.01338150 | 155 | 0.8445610 | 0.9191820 |

gene_258 | 17.95400 | -0.66579750 | 133 | 0.7472297 | 0.9191820 |

gene_549 | 55.86578 | 1.25876700 | 25 | 0.1040573 | 0.7359122 |

gene_891 | 69.81941 | 1.96711288 | 9 | 0.0245851 | 0.4578919 |

gene_1450 | 32.99729 | 0.09786426 | 68 | 0.4610200 | 0.9191820 |

gene_742 | 28.62281 | -0.12420298 | 79 | 0.5494227 | 0.9191820 |

The following tutorial video demonstrates how to run the
`ExIR`

model on a sample experimental data.

You can also computationally simulate knockout and/or up-regulation of the top candidate features outputted by ExIR to evaluate the impact of their manipulations on the flow of information/signaling and integrity of the network prior to taking them to your lab bench.

The `exir.vis`

is a function for the visualization of the
output of the ExIR model. The function simply gets
the output of the ExIR model as a single argument and returns a plot of
the top 10 prioritized features of all classes. Here, we visualize the
top five candidates of the results of the `ExIR`

model
obtained in the previous step .

However, a complete flexibility (list of arguments) has been provided for the adjustment of all of the visual features of the plot and selection of the desired classes, feature types, and the number of top candidates.

The following tutorial video demonstrates how to visualize the
results of `ExIR`

model.

A shiny app has also been developed for Running the ExIR model,
visualization of its results as well as computational simulation of
knockout and/or up-regulation of its top candidate outputs, which is
accessible using the following command.

`influential::runShinyApp("ExIR")`

You can also access the shiny app online at the Influential Software Package
server.

The `comp_manipulate`

is a function for the simulation of
feature (gene, protein, etc.) knockout and/or up-regulation in cells.
This function works based on the SIRIR (SIR-based
Influence Ranking) model and could be applied on the output of the ExIR model or any other independent association
network. For feature (gene/protein/etc.) knockout the SIRIR model is used to remove the feature from the
network and assess its impact on the flow of information (signaling)
within the network. On the other hand, in case of up-regulation a node
similar to the desired node is added to the network with exactly the
same connections (edges) as of the original node. Next, the SIRIR model is used to evaluate the difference in the
flow of information/signaling after adding (up-regulating) the desired
feature/node compared with the original network. In case you are
applying this function on the output of ExIR model,
you may note that as the gene/protein knockout would impact on the
integrity of the under-investigation network as well as the networks of
other overlapping biological processes/pathways, it is recommended to
select those features that simultaneously have the highest (most
significant) ExIR-based rank and lowest knockout
rank. In contrast, as the up-regulation would not affect the integrity
of the network, you may select the features with highest (most
significant) ExIR-based and up-regulation-based
ranks. Altogether, it is recommended to select the features with the
highest (most significant) ExIR-based (major drivers
or mediators of the under-investigation biological process/disease) and
*Up-regulation*-based (having higher impact on the signaling
within the under-investigation network when up-regulated) ranks, but
with the lowest *Knockout*-based rank (having the lowest
disturbance to the under-investigation as well as other overlapping
networks). Below is an example of running this function on the same ExIR output generated above.

```
# Select which genes to knockout
set.seed(60)
ko_vertices <- sample(igraph::as_ids(V(My.exir$Graph)), size = 5)
# Select which genes to up-regulate
set.seed(1234)
upregulate_vertices <- sample(igraph::as_ids(V(My.exir$Graph)), size = 5)
Computational_manipulation <- comp_manipulate(exir_output = My.exir,
ko_vertices = ko_vertices,
upregulate_vertices = upregulate_vertices,
beta = 0.5, gamma = 1, no.sim = 100, seed = 1234)
```

Have a look at the heads of the output tables:

**Knockout**

Feature_name | Rank | Manipulation_type | |
---|---|---|---|

2 | gene_280 | 1 | Knockout |

1 | gene_4798 | 2 | Knockout |

4 | gene_276 | 3 | Knockout |

3 | gene_16459 | 4 | Knockout |

5 | gene_7535 | 5 | Knockout |

**Up-regulation**

Feature_name | Rank | Manipulation_type |
---|---|---|

gene_6433 | 1 | Up-regulation |

gene_8426 | 1 | Up-regulation |

gene_6687 | 1 | Up-regulation |

gene_1274 | 1 | Up-regulation |

gene_11555 | 1 | Up-regulation |

**Combined**

Feature_name | Rank | Manipulation_type | |
---|---|---|---|

2 | gene_280 | 1 | Knockout |

1 | gene_4798 | 2 | Knockout |

4 | gene_276 | 3 | Knockout |

3 | gene_16459 | 4 | Knockout |

11 | gene_6433 | 5 | Up-regulation |

21 | gene_8426 | 5 | Up-regulation |

31 | gene_6687 | 5 | Up-regulation |

41 | gene_1274 | 5 | Up-regulation |

51 | gene_11555 | 5 | Up-regulation |

5 | gene_7535 | 10 | Knockout |

Csardi G., Nepusz T.

*The igraph software package for complex network research*. InterJournal. 2006; (1695).↩︎Salavaty A, Rezvani Z, Najafi A.

*Survival analysis and functional annotation of long non-coding RNAs in lung adenocarcinoma*. J Cell Mol Med. 2019;23:5600–5617. (PMID: 31211495)↩︎Maslov S., Sneppen K.

*Specificity and stability in topology of protein networks*. Science. 2002; 296: 910-913 (PMID:11988575)↩︎Salavaty A, Ramialison M, Currie PD.

*Integrated Value of Influence: An Integrative Method for the Identification of the Most Influential Nodes within Networks*. Patterns. 2020.08.14. (Read online)↩︎