Centrality Measures in Semantica: Degree, PageRank, and Graph Analysis

Semantica provides five built-in centrality measures—Degree, Betweenness, Closeness, Eigenvector, and PageRank—accessible through the CentralityCalculator class in semantica/kg/centrality_calculator.py.

The semantica-agi/semantica repository ships with a comprehensive knowledge-graph engine that includes native support for graph-theoretic analysis. Understanding the available centrality measures enables developers to quantify node importance, identify key entities, and analyze relationship networks without external dependencies.

Available Centrality Measures in Semantica

The CentralityCalculator class implements a suite of classical graph algorithms. The supported_centrality_types list defined at lines 7-13 in semantica/kg/centrality_calculator.py enumerates each available measure.

Degree Centrality

Degree centrality counts the number of direct connections of a node and normalizes that count by the maximum possible degree in the graph. This metric identifies highly connected "hub" entities within the knowledge graph. Access this measure via the calculate_degree_centrality() method.

Betweenness Centrality

Betweenness centrality quantifies how often a node lies on the shortest paths between other node pairs. Nodes with high betweenness act as bridges or gatekeepers within the network structure. Compute this using calculate_betweenness_centrality().

Closeness Centrality

Closeness centrality inversely relates to the average shortest-path distance from a node to all other reachable nodes. This measure identifies entities that can efficiently spread information through the graph. Invoke calculate_closeness_centrality() to obtain these scores.

Eigenvector Centrality

Eigenvector centrality scores nodes based on the importance of their neighbors, using power-iteration techniques on the adjacency matrix. This metric captures the influence of well-connected entities beyond just their direct connection counts. Use calculate_eigenvector_centrality() for this analysis.

PageRank

PageRank implements Google's random-walk ranking algorithm, evaluating node importance through iterative link-structure analysis with configurable damping factors. This is particularly effective for directed graphs and citation networks. Call calculate_pagerank() with optional damping_factor (default 0.85) and max_iterations parameters.

Computing Centrality Measures

Calculating Individual Metrics

Import CentralityCalculator from semantica/kg/centrality_calculator.py and instantiate the calculator to compute specific centrality scores:

from semantica.kg.centrality_calculator import CentralityCalculator

# Load or build a graph in Semantica format (dict with "entities" & "relationships")

graph = {...}

calc = CentralityCalculator()

# Degree centrality

degree = calc.calculate_degree_centrality(graph)
print("Top node by degree:", degree["rankings"][0])

# Betweenness centrality

betweenness = calc.calculate_betweenness_centrality(graph)
print("Node with highest betweenness:", betweenness["rankings"][0])

# Closeness centrality

closeness = calc.calculate_closeness_centrality(graph)
print("Most central (closeness):", closeness["rankings"][0])

# Eigenvector centrality

eigen = calc.calculate_eigenvector_centrality(graph)
print("Highest eigenvector score:", eigen["rankings"][0])

# PageRank with custom parameters

pagerank = calc.calculate_pagerank(
    graph, 
    damping_factor=0.85, 
    max_iterations=30
)
print("Highest PageRank:", pagerank["rankings"][0])

Batch Processing with calculate_all_centrality

The calculate_all_centrality() method runs every supported centrality algorithm in a single pass and returns a unified results dictionary. This approach minimizes redundant shortest-path calculations when multiple metrics are required.

from semantica.kg.centrality_calculator import CentralityCalculator

calc = CentralityCalculator()
all_results = calc.calculate_all_centrality(graph)

# Access individual measures from the combined output

degree_top = all_results["centrality_measures"]["degree"]["rankings"][0]
betweenness_top = all_results["centrality_measures"]["betweenness"]["rankings"][0]
closeness_top = all_results["centrality_measures"]["closeness"]["rankings"][0]
eigenvector_top = all_results["centrality_measures"]["eigenvector"]["rankings"][0]

Algorithm Registry and Discovery

The algorithm_registry in semantica/kg/registry.py (lines 58-63) registers PageRank as a first-class centrality algorithm, making it discoverable through the registry's introspection capabilities. Query registered algorithms programmatically:

from semantica.kg.registry import algorithm_registry

centrality_algos = algorithm_registry.list_category("centrality")
print("Registered centrality algorithms:", centrality_algos)

# Output: ['pagerank']

This registration pattern allows the system to treat PageRank as a plugin-capable component while maintaining consistency with Semantica's broader algorithm management framework.

Summary

• Semantica implements five centrality measures through CentralityCalculator: Degree, Betweenness, Closeness, Eigenvector, and PageRank.
• Each measure exposes a dedicated calculate_*() method in semantica/kg/centrality_calculator.py.
• The calculate_all_centrality() convenience method computes all metrics simultaneously for efficiency.
• PageRank is additionally registered in semantica/kg/registry.py (lines 58-63) as a discoverable centrality algorithm.
• All methods accept standard Semantica graph dictionaries containing "entities" and "relationships" keys.

Frequently Asked Questions

What centrality measures are available in Semantica?

Semantica provides five centrality measures: Degree, Betweenness, Closeness, Eigenvector, and PageRank. These are implemented in the CentralityCalculator class located at semantica/kg/centrality_calculator.py and enumerated in the supported_centrality_types list.

How do I compute all centrality measures at once?

Call the calculate_all_centrality() method on a CentralityCalculator instance. This executes all five algorithms in one pass and returns a dictionary with results under the "centrality_measures" key, organized by measure name (e.g., "degree", "betweenness", "pagerank").

What parameters does PageRank support in Semantica?

The calculate_pagerank() method accepts damping_factor (float, typically 0.85) and max_iterations (int) parameters. These control the random-walk probability and convergence limits respectively, matching the standard Google PageRank implementation.

Where can I find test examples for centrality calculations?

Reference implementations appear in tests/kg/test_provenance_workflows.py, which exercises each centrality method with provenance tracking, and tests/kg/test_real_world_scenarios.py, which demonstrates combined calculations on academic citation networks using real-world knowledge graph structures.

{
  "mcpServers": {
    "instagit": {
      "command": "npx",
      "args": ["-y", "instagit@latest"]
    }
  }
}