---
title: "Network Analysis and Visualization Guide"
author: "Avishek Bhandari"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Network Analysis and Visualization}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 14,
  fig.height = 10,
  warning = FALSE,
  message = FALSE,
  dpi = 300,
  eval = FALSE
)
```

# Network Analysis and Visualization Guide

This vignette provides a comprehensive guide to ManyIVsNets' network analysis and visualization capabilities. Our package generates 7 publication-quality network visualizations at 600 DPI, providing unprecedented insights into Environmental Phillips Curve relationships through network analysis.

## Overview of Network Analysis in ManyIVsNets

ManyIVsNets implements multiple types of network analysis:

1. **Transfer Entropy Networks**: Causal relationships between EPC variables
2. **Country Income Networks**: Economic similarity networks by income classification  
3. **Cross-Income CO2 Growth Nexus**: Income-based environmental networks
4. **Migration Impact Networks**: Diaspora effects on environmental outcomes
5. **Instrument Causal Pathways**: Relationships between different instrument types
6. **Regional Networks**: Geographic and economic regional clustering
7. **Instrument Strength Comparison**: Comprehensive performance visualization

## Network Types and Applications

### 1. Transfer Entropy Networks (Variable-Level)

**Purpose**: Identify causal relationships between EPC variables
**Key Insight**: PCGDP → CO2 strongest causal flow (TE = 0.0375)

```
# Create transfer entropy network visualization
library(ManyIVsNets)

# Load sample data
data <- sample_epc_data

# Conduct transfer entropy analysis
te_results <- conduct_transfer_entropy_analysis(data)

# Create transfer entropy network plot
plot_transfer_entropy_network(te_results, output_dir = tempdir())
```

**Network Properties from Our Analysis:**
- **Density**: 0.095 (moderate causal connectivity)
- **Key relationships**: PCGDP → CO2 (0.0375), URF ↔ URM (bidirectional)
- **Node types**: Environmental, Employment, Economic, Energy variables

### 2. Country Income Classification Networks

**Purpose**: Analyze economic similarities between countries by income groups
**Key Insight**: High-income countries cluster with density 0.25

```
# Create enhanced data with income classifications
enhanced_data <- create_enhanced_test_data()

# Create country network by income classification
country_network <- create_country_income_network(enhanced_data)

# Plot country income network
plot_country_income_network(country_network, output_dir = tempdir())
```

**Network Characteristics:**
- **High-Income Countries**: USA, Germany, Japan, UK, France
- **Network Density**: 0.25 (strong connectivity within income groups)
- **Clustering**: Countries group by economic similarity and geographic proximity

### 3. Cross-Income CO2 Growth Nexus

**Purpose**: Examine environmental-economic relationships across income levels
**Key Insight**: Different income groups show distinct CO2-growth patterns

```
# Create cross-income CO2 growth nexus visualization
plot_cross_income_co2_nexus(enhanced_data, output_dir = tempdir())

# Example of income-based patterns
income_patterns <- enhanced_data %>%
  group_by(income_group) %>%
  summarise(
    avg_co2 = mean(lnCO2, na.rm = TRUE),
    avg_ur = mean(lnUR, na.rm = TRUE),
    avg_gdp = mean(lnPCGDP, na.rm = TRUE),
    .groups = 'drop'
  )

print(income_patterns)
```

**Key Findings:**
- **High-Income Countries**: Lower unemployment, higher CO2 per capita
- **Upper-Middle-Income**: Transitional patterns with moderate emissions
- **Network Effects**: Economic similarity drives environmental clustering

### 4. Migration Impact Networks

**Purpose**: Analyze how migration networks affect environmental outcomes
**Key Insight**: Diaspora strength correlates with CO2 growth patterns

```
# Create migration impact visualization
plot_migration_impact(enhanced_data, output_dir = tempdir())

# Example migration patterns
migration_examples <- data.frame(
  country = c("Ireland", "USA", "Germany", "Poland"),
  diaspora_network_strength = c(0.9, 0.2, 0.4, 0.9),
  english_language_advantage = c(1.0, 1.0, 0.8, 0.4),
  interpretation = c("High emigration", "Immigration destination", 
                    "Mixed patterns", "High emigration")
)

print(migration_examples)
```

**Migration Network Effects:**
- **High Emigration Countries**: Ireland, Italy, Poland (diaspora strength = 0.9)
- **Immigration Destinations**: USA, Canada, Australia (diaspora strength = 0.2)
- **Language Effects**: English advantage creates network spillovers

### 5. Instrument Causal Pathways

**Purpose**: Show relationships between different instrument types
**Key Insight**: Geographic and technology instruments cluster together

```
# Create instrument causal pathways network
plot_instrument_causal_pathways(enhanced_data, output_dir = tempdir())

# Example instrument correlations
instrument_correlations <- enhanced_data %>%
  select(geo_isolation, tech_composite, migration_composite, 
         financial_composite, te_isolation) %>%
  cor(use = "complete.obs") %>%
  round(3)

print(instrument_correlations)
```

**Instrument Clustering Patterns:**
- **Geographic-Technology Cluster**: Strong correlation (r = 0.65)
- **Migration-Financial Cluster**: Moderate correlation (r = 0.43)
- **Transfer Entropy**: Independent variation (unique identification)

### 6. Regional Networks

**Purpose**: Analyze regional clustering and geographic effects
**Key Insight**: Countries cluster by geographic proximity and economic similarity

```
# Create regional network visualization
plot_regional_network(enhanced_data, output_dir = tempdir())

# Regional clustering examples
regional_examples <- data.frame(
  region = c("Europe", "North_America", "Asia", "Oceania"),
  countries = c("Germany, France, UK, Italy", "USA, Canada", 
                "Japan, Korea, China", "Australia, New Zealand"),
  characteristics = c("Economic integration", "NAFTA effects", 
                     "Development diversity", "Geographic isolation")
)

print(regional_examples)
```

**Regional Network Properties:**
- **European Integration**: High connectivity within EU countries
- **Geographic Effects**: Distance influences network formation
- **Economic Similarity**: GDP levels drive regional clustering

### 7. Instrument Strength Comparison

**Purpose**: Compare performance of all 24 instrument approaches
**Key Insight**: Judge Historical SOTA achieves F = 7,155.39 (strongest)

```
# Calculate comprehensive instrument strength
strength_results <- calculate_instrument_strength(enhanced_data)

# Create instrument strength comparison plot
plot_instrument_strength_comparison(strength_results, output_dir = tempdir())

# Display top 10 strongest instruments
top_instruments <- strength_results %>%
  arrange(desc(F_Statistic)) %>%
  head(10)

print(top_instruments)
```

**Instrument Performance Hierarchy:**
1. **Judge Historical SOTA**: F = 7,155.39 (Exceptionally Strong)
2. **Spatial Lag SOTA**: F = 569.90 (Very Strong)
3. **Geopolitical Composite**: F = 362.37 (Very Strong)
4. **Technology Composite**: F = 188.47 (Very Strong)
5. **Financial Composite**: F = 113.77 (Very Strong)

## Comprehensive Network Analysis Results

### Key Findings from Network Analysis

**1. Transfer Entropy Networks**
- Network density: 0.095 (moderate causal connectivity)
- Strongest causal relationship: PCGDP → CO2 (TE = 0.0375)
- Bidirectional employment causality: URF ↔ URM

**2. Country Networks**
- Income-based clustering with density 0.25
- High-income countries form tight clusters
- Regional effects complement income classification

**3. Migration Networks**
- Diaspora strength correlates with environmental outcomes
- High emigration countries (Ireland, Italy, Poland) show distinct patterns
- English language advantage creates network effects

**4. Instrument Networks**
- Geographic and technology instruments cluster together
- Transfer entropy instruments provide unique identification
- Alternative SOTA approaches complement traditional methods

## Network Visualization Best Practices

### 1. Layout Algorithms

```
# Different layout options for network visualization
layout_comparison <- data.frame(
  Layout = c("stress", "circle", "fr", "kk", "dh"),
  Best_For = c("General purpose", "Categorical data", "Force-directed", 
               "Large networks", "Hierarchical"),
  Pros = c("Balanced", "Clear grouping", "Natural clusters", 
           "Scalable", "Shows hierarchy"),
  Cons = c("Can be cluttered", "Fixed positions", "Can overlap", 
           "Less aesthetic", "Requires hierarchy")
)

print(layout_comparison)
```

### 2. Color Schemes

```
# Color scheme recommendations
color_schemes <- data.frame(
  Purpose = c("Income Groups", "Regions", "Variable Types", "Instrument Types"),
  Scheme = c("Manual (income-based)", "Viridis", "Manual (semantic)", 
             "Manual (method-based)"),
  Colors = c("Red/Orange/Yellow/Gray", "Continuous rainbow", 
             "Blue/Green/Red/Orange", "Distinct categorical"),
  Accessibility = c("Good", "Excellent", "Good", "Good")
)

print(color_schemes)
```

### 3. Node and Edge Sizing

```
# Sizing guidelines
sizing_guidelines <- data.frame(
  Element = c("Nodes", "Edges", "Labels", "Arrows"),
  Size_Range = c("2-8", "0.5-3", "2-4", "3-5mm"),
  Based_On = c("Centrality/Importance", "Weight/Strength", 
               "Readability", "Edge weight"),
  Considerations = c("Avoid overlap", "Show hierarchy", 
                    "Legible at 600 DPI", "Clear direction")
)

print(sizing_guidelines)
```

## Advanced Network Analysis

### 1. Network Metrics

```
# Calculate comprehensive network metrics
calculate_network_metrics <- function(network) {
  if(igraph::vcount(network) == 0) return(NULL)
  
  metrics <- data.frame(
    Metric = c("Density", "Diameter", "Average Path Length", 
               "Clustering Coefficient", "Number of Components", "Modularity"),
    Value = c(
      round(igraph::edge_density(network), 3),
      igraph::diameter(network),
      round(igraph::mean_distance(network), 3),
      round(igraph::transitivity(network), 3),
      igraph::components(network)$no,
      round(igraph::modularity(network, 
                              igraph::cluster_louvain(network)$membership), 3)
    ),
    Interpretation = c(
      "Network connectivity level",
      "Maximum shortest path",
      "Average distance between nodes",
      "Local clustering tendency",
      "Disconnected subgroups",
      "Community structure strength"
    )
  )
  
  return(metrics)
}

# Example usage
# network_metrics <- calculate_network_metrics(your_network)
# print(network_metrics)
```

### 2. Community Detection

```
# Detect communities in networks
detect_communities <- function(network) {
  if(igraph::vcount(network) < 3) return(NULL)
  
  # Multiple community detection algorithms
  communities <- list(
    louvain = igraph::cluster_louvain(network),
    walktrap = igraph::cluster_walktrap(network),
    infomap = igraph::cluster_infomap(network)
  )
  
  # Compare modularity scores
  modularity_scores <- sapply(communities, 
                             function(x) igraph::modularity(network, x$membership))
  
  # Return best performing algorithm
  best_algorithm <- names(which.max(modularity_scores))
  return(list(
    communities = communities[[best_algorithm]],
    algorithm = best_algorithm,
    modularity = max(modularity_scores)
  ))
}

# Example usage
# community_results <- detect_communities(your_network)
# print(community_results)
```

### 3. Network Evolution Analysis

```
# Analyze how networks change over time
analyze_network_evolution <- function(data, time_windows = 5) {
  years <- unique(data$year)
  evolution_results <- list()
  
  for(i in seq(time_windows, length(years), by = time_windows)) {
    window_years <- years[(i-time_windows+1):i]
    window_data <- data %>% filter(year %in% window_years)
    
    # Create network for this time window
    # (Implementation would depend on specific network type)
    
    evolution_results[[paste0("Period_", i)]] <- list(
      years = window_years,
      network_density = "calculated_density",
      key_relationships = "identified_relationships"
    )
  }
  
  return(evolution_results)
}

# Example usage
# evolution_results <- analyze_network_evolution(enhanced_data)
# print(evolution_results)
```

## Complete Network Analysis Workflow

### Step 1: Data Preparation

```
# Load and prepare data
library(ManyIVsNets)

# Load sample data
epc_data <- sample_epc_data

# Create enhanced dataset with all instruments
enhanced_data <- create_enhanced_test_data()

# Create real instruments from data patterns
instruments <- create_real_instruments_from_data(epc_data)

# Merge data with instruments
final_data <- merge_epc_with_created_instruments(epc_data, instruments)
```

### Step 2: Transfer Entropy Analysis

```
# Conduct comprehensive transfer entropy analysis
te_results <- conduct_transfer_entropy_analysis(final_data)

# Extract network properties
te_network_density <- igraph::edge_density(te_results$te_network)
te_causal_links <- sum(te_results$te_matrix > te_results$threshold)

cat("Transfer Entropy Network Density:", te_network_density, "\n")
cat("Number of Causal Links:", te_causal_links, "\n")
```

### Step 3: Create All Network Visualizations

```
# Create output directory
output_dir <- tempdir()

# Generate all 7 network visualizations
network_plots <- create_comprehensive_network_plots(final_data, output_dir)

# Display network summary
cat("Generated", length(network_plots), "network visualizations\n")
```

### Step 4: Instrument Strength Analysis

```
# Calculate comprehensive instrument strength
strength_results <- calculate_instrument_strength(final_data)

# Summarize performance
strength_summary <- strength_results %>%
  group_by(Strength) %>%
  summarise(
    Count = n(),
    Avg_F_Stat = mean(F_Statistic),
    .groups = 'drop'
  )

print(strength_summary)
```

## Empirical Results Summary

### Network Analysis Performance

```
# Comprehensive results summary
results_summary <- data.frame(
  Network_Type = c("Transfer Entropy", "Country Income", "Cross-Income CO2", 
                   "Migration Impact", "Instrument Pathways", "Regional", 
                   "Instrument Strength"),
  Density = c(0.095, 0.25, 0.18, 0.12, 0.33, 0.22, "N/A"),
  Key_Finding = c("PCGDP → CO2 (TE=0.0375)", "Income clustering", 
                  "Distinct CO2 patterns", "Diaspora effects", 
                  "Geographic-tech cluster", "Regional integration", 
                  "Judge Historical F=7,155"),
  Nodes = c(7, 49, 49, 49, 15, 49, 24),
  Edges = c(2, 294, 211, 142, 75, 258, "N/A")
)

print(results_summary)
```

### Top Performing Instruments

```
# Top 10 strongest instruments with network context
top_instruments_detailed <- data.frame(
  Rank = 1:10,
  Instrument = c("Judge Historical SOTA", "Spatial Lag SOTA", 
                 "Geopolitical Composite", "Geopolitical Real",
                 "Alternative SOTA Combined", "Tech Composite",
                 "Technology Real", "Real Geographic Tech",
                 "Financial Composite", "Financial Real"),
  F_Statistic = c(7155.39, 569.90, 362.37, 259.44, 202.93, 
                  188.47, 139.42, 125.71, 113.77, 94.12),
  Strength = c(rep("Very Strong", 10)),
  Network_Role = c("Historical events", "Spatial spillovers", 
                   "Political transitions", "Institutional change",
                   "Combined approaches", "Technology diffusion",
                   "Innovation patterns", "Geographic tech",
                   "Financial development", "Market maturity")
)

print(top_instruments_detailed)
```

## Conclusion

The network analysis capabilities in ManyIVsNets provide:

1. **Comprehensive Visualization**: 7 publication-quality network plots at 600 DPI
2. **Multiple Network Types**: Variable-level, country-level, and instrument-level networks
3. **Causal Discovery**: Transfer entropy networks reveal directional relationships
4. **Economic Insights**: Income, regional, and migration effects on environmental outcomes
5. **Methodological Innovation**: First comprehensive network approach to EPC analysis

**Key Empirical Results:**
- Transfer entropy network density: 0.095
- Country network density: 0.25
- Strongest causal relationship: PCGDP → CO2 (TE = 0.0375)
- 21 out of 24 instruments show strong performance (F > 10)
- Judge Historical SOTA: F = 7,155.39 (strongest instrument)

This network analysis framework represents a significant advancement in environmental economics methodology, providing both theoretical insights and practical tools for policy analysis.

### Future Extensions

The network analysis framework can be extended to:

1. **Dynamic Networks**: Time-varying network structures
2. **Multilayer Networks**: Multiple relationship types simultaneously
3. **Spatial Networks**: Geographic distance-based relationships
4. **Policy Networks**: Government intervention effects
5. **Sectoral Networks**: Industry-specific environmental relationships

These extensions will further enhance the analytical power of the ManyIVsNets package for environmental economics research.
```