Introduction to Network Analysis

Network analysis is a powerful tool used to study complex systems composed of interconnected elements, such as social networks, biological systems, or infrastructure networks. It allows researchers to understand the structure and dynamics of relationships between individual components within a system.

What is Network Analysis?

Network analysis involves representing a system as a network, which consists of nodes (representing entities) and edges (representing relationships or interactions between entities). By studying the patterns of connections and interactions within the network, researchers can gain insights into the underlying structure and behavior of the system.

Visualization

Visualization is crucial for understanding and interpreting network data. Network analysis often involves creating visual representations of the network using graphical techniques. These visualizations can range from simple node-and-edge diagrams to more complex layouts that highlight various properties of the network, such as node centrality or community structure.

Testing Accuracy

Assessing the accuracy of a network model involves comparing it to empirical data or evaluating its predictive performance. This can be done using statistical techniques such as goodness-of-fit tests, cross-validation, or comparing model predictions to observed outcomes.

Centrality

Centrality measures quantify the importance or influence of nodes within a network. Nodes with high centrality are often considered to be more central or influential within the network. Common centrality measures include degree centrality (number of connections), betweenness centrality (importance of a node in connecting other nodes), and closeness centrality (average distance to all other nodes).

Comparing Networks

Comparing networks involves assessing similarities or differences between two or more networks. This can be done by comparing their topological properties, such as degree distributions, average path lengths, or clustering coefficients. Additionally, specialized techniques exist for comparing networks with different node sets or edge weights.

R Packages for Network Analysis

The qgraph and netboot packages in R provide tools for visualizing and analyzing networks.

• qgraph: Particularly useful for creating high-quality network visualizations.
• netboot: Offers methods for bootstrapping network models to test their stability and accuracy.

By leveraging these packages, researchers can gain valuable insights into the structure and dynamics of complex systems through network analysis in R.

An Example

In this example, we’ll perform network analysis on a dataset of Covid-19 infection symptoms using R. We’ll visualize the correlation network, test the significance of correlations, and estimate the network structure.

# Load required libraries
library(corrplot)
library(corpcor)  # for partial correlation
library(qgraph) # for visualization
library(bootnet) # to estimate stability
library(gridExtra)  #to use grid.arrange
library(QuantPsyc)
library(energy)

The data preparation

# Define COVID-19 symptoms
symptoms <- c("Fever", "Cough", "Shortness of breath", "Fatigue", "Muscle or body aches",
              "Headache", "Sore throat", "Loss of taste or smell", "Congestion or runny nose",
              "Nausea or vomiting")

# Generate random data for correlation between symptoms
set.seed(123)
num_symptoms <- length(symptoms)

Estimating and Visualizing Network Structure

correlation_matrix <- matrix(runif(num_symptoms^2, min = -0.5, max = 0.5), nrow = num_symptoms)

# Set diagonal to 1
diag(correlation_matrix) <- 1

# Estimate the network structure
network <- estimateNetwork(correlation_matrix, default = "pcor")

# Plot the estimated network
#png("network.png",units="cm", width=12, height=12,res=500)
plot(network, labels = symptoms)
#dev.off()

Centrality and Accuracy

#png("centrality.png",units="cm", width=12, height=12,res=500)
centralityPlot(
  list(Complete = network),
  include = c("Strength", "Closeness", "Betweenness"),orderBy = "Strength")
#dev.off()

References

Silge, Julia, and David Robinson. 2017. Text Mining with r: A Tidy Approach. “ O’Reilly Media, Inc.” GoogleScholar