Using PageRank for Financial Network Analysis

Business Case: Identifying Key Financial Entities

In financial networks, not all entities are equally important. Some play central roles in moving money, influencing other entities, or connecting different parts of the network. PageRank can help identify these crucial entities by analyzing: - Transaction patterns - Money flow dynamics - Network influence - Systemic importance

Originally developed by Google for ranking web pages, PageRank has valuable applications in financial analysis because it can reveal entities that are: - Central to money movement networks - Potential systemic risk sources - Key players in financial markets - Important intermediaries in transaction chains

Implementation with IbisGraph

Here's how to implement PageRank analysis using IbisGraph while keeping all processing within your data warehouse:

import ibis
import ibisgraph as ig

# Connect to your data warehouse (e.g., PostgreSQL, Snowflake, etc.)
conn = ibis.postgres.connect(
    host='your_host',
    database='your_db',
    user='your_user',
    password='your_password'
)

# Assume we have a transactions table with columns:
# - from_account: source account
# - to_account: destination account
# - amount: transaction amount
# - date: transaction date

# Load transaction data
transactions = conn.table('transactions')

# Create a weighted graph based on transaction amounts
graph = ig.Graph(
    transactions,
    source_col='from_account',
    target_col='to_account',
    weight_col='amount'  # Weight edges by transaction amounts
)

# Calculate PageRank scores
pagerank_scores = ig.centrality.page_rank(
    graph,
    alpha=0.85,  # Standard damping factor
    max_iters=100,  # Maximum iterations
    tol=1e-6  # Convergence tolerance
)

# Join with account information for analysis
account_info = conn.table('account_info')
ranked_accounts = (
    pagerank_scores
    .join(
        account_info,
        pagerank_scores.node_id == account_info.account_id
    )
    .select([
        'account_id',
        'account_type',
        'business_name',
        'pagerank',
        account_info.total_volume,  # Assuming this exists
    ])
    .order_by(ibis.desc('pagerank'))
)

Advanced Analysis Techniques

Time-Window Analysis

Track changes in entity importance over time:

# Function to create graph for a specific time window
def get_time_window_pagerank(start_date, end_date):
    window_transactions = transactions.filter(
        (transactions.date >= start_date) &
        (transactions.date < end_date)
    )

    window_graph = ig.Graph(
        window_transactions,
        source_col='from_account',
        target_col='to_account',
        weight_col='amount'
    )

    return ig.centrality.page_rank(window_graph)

# Compare monthly PageRank scores
current_month = get_time_window_pagerank('2024-03-01', '2024-04-01')
previous_month = get_time_window_pagerank('2024-02-01', '2024-03-01')

# Analyze changes
rank_changes = (
    current_month
    .join(
        previous_month,
        current_month.node_id == previous_month.node_id
    )
    .select([
        'node_id',
        current_month.pagerank.name('current_rank'),
        previous_month.pagerank.name('previous_rank'),
        (current_month.pagerank - previous_month.pagerank).name('rank_change')
    ])
    .order_by(ibis.desc('rank_change'))
)

Risk-Weighted PageRank

Incorporate risk factors into the analysis:

# Assume we have risk scores for transactions
risk_weighted_txns = transactions.mutate(
    risk_weight=transactions.amount * transactions.risk_score
)

# Create risk-weighted graph
risk_graph = ig.Graph(
    risk_weighted_txns,
    source_col='from_account',
    target_col='to_account',
    weight_col='risk_weight'
)

# Calculate risk-weighted PageRank
risk_pagerank = ig.centrality.page_rank(risk_graph)

Applications in Financial Analysis

1. Systemic Risk Assessment

# Identify systemically important entities
systemic_entities = (
    pagerank_scores
    .filter(pagerank_scores.pagerank > pagerank_scores.pagerank.mean() + 2 * pagerank_scores.pagerank.std())
    .join(account_info, 'node_id')
    .select([
        'node_id',
        'business_name',
        'account_type',
        'pagerank',
        'total_volume'
    ])
)

2. Money Laundering Detection

# Combine PageRank with transaction patterns
suspicious_entities = (
    pagerank_scores
    .join(
        transactions.group_by('from_account')
        .aggregate([
            transactions.amount.count().name('tx_count'),
            transactions.amount.mean().name('avg_amount')
        ]),
        pagerank_scores.node_id == transactions.from_account
    )
    .filter(
        (pagerank_scores.pagerank > 0.01) &  # High influence
        (transactions.tx_count > 1000) &      # High activity
        (transactions.avg_amount < 1000)      # Small transactions
    )
)

3. Market Influence Analysis

# Analyze market maker influence
market_makers = (
    pagerank_scores
    .join(account_info, 'node_id')
    .filter(account_info.account_type == 'MARKET_MAKER')
    .select([
        'node_id',
        'business_name',
        'pagerank',
        account_info.daily_volume,
        account_info.num_counterparties
    ])
    .order_by(ibis.desc('pagerank'))
)

Benefits of Using IbisGraph for PageRank Analysis

Scalability
- Processes large transaction networks efficiently
- Handles millions of transactions and entities
- Leverages data warehouse computational resources
Data Security
- Keeps sensitive financial data within your secure environment
- Maintains regulatory compliance
- Provides audit trail for analyses
Real-time Analysis
- Can be updated as new transactions occur
- Supports continuous monitoring
- Enables quick response to changes in network dynamics
Integration Capabilities
- Works with existing data warehouse infrastructure
- Combines easily with other analysis tools
- Supports multiple data sources

Practical Use Cases

Regulatory Compliance
- Identify systematically important financial institutions
- Monitor market concentration
- Track changes in financial network structure
Risk Management
- Assess counterparty exposure
- Monitor network dependencies
- Identify potential cascading failures
Business Intelligence
- Find key market participants
- Analyze customer importance
- Track market influence
Fraud Detection
- Identify unusual influence patterns
- Detect hidden relationships
- Monitor network anomalies

This approach provides a powerful tool for understanding complex financial networks while maintaining data security and leveraging existing infrastructure. It can be integrated into various analysis workflows and supports both strategic and operational decision-making.