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 datasetset.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 genescorrelation_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:
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.
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 dataMyData <- coexpression.data # Reconstructing the graphMy_graph <-graph_from_data_frame(MyData) # Extracting the verticesMy_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
4.2 Degree
centrality
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 dataMyData <- coexpression.data # Reconstructing the graphMy_graph <-graph_from_data_frame(MyData) # Extracting the verticesGraphVertices <-V(My_graph) # Calculating degree centralityMy_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.
4.3 Betweenness
centrality
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.
Betweenness centrality could be also calculated for directed
and/or weighted graphs via specifying the directed
and weights parameters, respectively.
4.4 Neighborhood
connectivity
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 paper3 in 2002
and is for the first time calculable in R environment via the
influential package.
Neighborhood connectivity could be also calculated for
directed graphs via specifying the mode
parameter.
4.5 H-index
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.
H-index could be also calculated for directed graphs via
specifying the mode parameter.
4.6 Local H-index
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 dataMyData <- coexpression.data # Reconstructing the graphMy_graph <-graph_from_data_frame(MyData) # Extracting the verticesGraphVertices <-V(My_graph) # Calculating Local H-indexlh.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.
4.7 Collective
Influence
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.
Collective Influence could be also calculated for directed
graphs via specifying the mode parameter.
4.8 ClusterRank
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.
5 Assessment of the
association of centrality measures
5.1 Conditional
probability of deviation from means
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.
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.
5.2 Nature of association
(considering dependent and independent)
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
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
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 package4: 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.
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.
5.3 Nature of association
(without considering dependence direction)
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
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.
6 Identification of the
most 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.
6.1 Integrated Value of
Influence (IVI) from centrality measures
6.2 Integrated Value of
Influence (IVI) from a graph
# Preparing the dataMyData <- coexpression.data # Reconstructing the graphMy_graph <-graph_from_data_frame(MyData) # Extracting the verticesGraphVertices <-V(My_graph) # Calculation of IVIMy.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
paper5 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.
6.3 Network
visualization
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 graphset.seed(70)My_graph <- igraph::sample_gnm(n =50, m =120, directed =TRUE)# Calculating the IVI valuesMy_graph_IVI <-ivi(My_graph, directed =TRUE)# Visualizing the graph based on IVI valuesMy_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).
6.4 IVI shiny app
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.
7 Identification of the
most important network spreaders
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.
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.
8 Identification of the
most important network hubs
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.
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.
9 Ranking the influence
of nodes on the topology of a network based on the 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 graphMy_graph <-sif2igraph(Path ="Sample_SIF.sif") # Extracting the verticesGraphVertices <-V(My_graph) # Calculation of influence rankInfluence.Ranks <-sirir(graph = My_graph, vertices = GraphVertices, beta =0.5, gamma =1, no.sim =10, seed =1234)
10 Experimental
data-based classification and ranking of top candidate features
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 datagene.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)
10.1 Assembling the
Diff_data
Use the function diff_data.assembly to automatically
generate the Diff_data table for the ExIR model.
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
10.2 Preparing the
Exptl_data
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 distributionMyExptl_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.
Finally, prepare the other required input data for the
ExIR model.
#The table of differential/regression previously preparedmy_Diff_data#The column indices of differential values in the Diff_data tableDiff_value <-c(1,3) #The column indices of regression values in the Diff_data tableRegr_value <-5#The column indices of significance (P-value/FDR) values in # the Diff_data tableSig_value <-c(2,4) #The matrix/data frame of normalized experimental# data previously preparedMyExptl_data#The name of the column delineating the conditions of# samples in the Exptl_data matrixCondition_colname <-"condition"#The desired list of featuresset.seed(60)MyDesired_list <-sample(gene.names, size =500) #Optional#Running the ExIR modelMy.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.
10.4 ExIR
visualization
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 .
My.exir.Vis <-exir.vis(exir.results = My.exir, n =5,y.axis.title ="Gene")My.exir.Vis
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.
10.5 ExIR shiny app
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 knockoutset.seed(60)ko_vertices <-sample(igraph::as_ids(V(My.exir$Graph)), size =5)# Select which genes to up-regulateset.seed(1234)upregulate_vertices <-sample(igraph::as_ids(V(My.exir$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)
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)↩︎
