Introduction
Graph-Based Analysis uses graph theory algorithms to verify the structural integrity of digital engineering models. It checks if the model’s connections form a valid structure, like ensuring there are no circular dependencies in the analysis workflow.
Overview
Graph-Based Analysis is one of three verification approaches within the Semantic System Verification Layer (SSVL), used to ensure models are well-formed and consistent. It specifically verifies requirements related to the structural organization of the System of Analysis (SoA) by treating the SoA as a directed graph.
The graph representation of the SoA enables leveraging of graph-based algorithms from computer science to verify structural requirements. This approach complements the other two SSVL approaches: - Open World Analysis (using Description Logic reasoning) - Closed World Analysis (using SHACL constraints)
Graph-Based Analysis is particularly valuable for verifying requirements that involve the structure of connections between model elements, such as ensuring the SoA forms a Directed Acyclic Graph (DAG).
| Graph-Based Analysis is essential for verifying requirements that cannot be adequately checked using Open World or Closed World approaches alone, especially those involving graph structure and connectivity patterns. |
Position in Knowledge Hierarchy
Broader concepts: - SSVL (is-a)
Narrower concepts: - DAG (is-a)
Details
Graph-Based Analysis works by transforming ontology-aligned data into a graph representation and then applying graph algorithms to verify model requirements. The process involves:
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Extracting the relevant subgraph from the ontology-aligned data using SPARQL queries
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Converting the extracted data into a format suitable for graph analysis tools
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Applying graph algorithms to verify specific structural requirements
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Interpreting the results to determine if the model meets the specified requirements
The most common requirement verified through Graph-Based Analysis is: - Requirement 10: "SoA shall form a Directed Acyclic Graph (DAG) when ordered by sequence"
This requirement ensures that the analysis workflow has a clear sequence without circular dependencies, which is critical for proper execution of the analysis.
| The SoA graph is derived from the Assessment Flow Diagram (AFD), which represents the sequence of analysis steps and how data flows between them. |
Graph Representation of SoA
The SoA can be represented as a directed graph (digraph) where: - Nodes represent model elements (e.g., analysis models, value properties) - Directed edges represent connections between these elements (e.g., data flow from one analysis to another)
This graph representation enables the use of standard graph algorithms to verify structural requirements.
| When implementing Graph-Based Analysis, it’s important to ensure the graph representation accurately reflects the intended analysis workflow. Inaccurate graph construction can lead to false positives or negatives in verification. |
Tooling for Graph-Based Analysis
The primary tool used for Graph-Based Analysis in the context of Digital Engineering is NetworkX, a Python library for network analysis. NetworkX provides a rich set of algorithms for analyzing graph structures.
The workflow for Graph-Based Analysis typically involves: 1. Using SPARQL to extract relevant subgraphs from the ontology-aligned data 2. Converting the SPARQL results into a format compatible with NetworkX 3. Applying NetworkX algorithms to verify requirements 4. Reporting the verification results
| NetworkX is particularly well-suited for this task because it provides efficient implementations of graph algorithms and integrates well with Python’s data analysis ecosystem. |
Practical applications and examples
Let’s walk through a practical example of implementing Graph-Based Analysis for the "SoA shall form a Directed Acyclic Graph" requirement using NetworkX.
Example: Verifying DAG Structure
The following Python code demonstrates how to check if a graph is a DAG using NetworkX:
import networkx as nx
from rdflib import Graph, Namespace
from rdflib.namespace import RDF
= Load the ontology-aligned data (triplestore)
g = Graph()
g.parse("soa_data.ttl", format="turtle")
= Define the namespace for the SoA
SOA = Namespace("http://example.org/soa#")
= Extract nodes and edges from the ontology
nodes = []
edges = []
= SPARQL query to extract the SoA graph structure
query = """
SELECT ?source ?target
WHERE {
?source a ?type .
?target a ?type .
?source <http://example.org/soa#hasConnection> ?target .
}
"""
= Execute the query and populate the graph
for row in g.query(query):
source = str(row[0])
target = str(row[1])
nodes.append(source)
nodes.append(target)
edges.append((source, target))
= Create a NetworkX graph
G = nx.DiGraph()
G.add_nodes_from(nodes)
G.add_edges_from(edges)
= Check if the graph is a DAG
is_dag = nx.is_directed_acyclic_graph(G)
if is_dag:
print("Verification successful: SoA forms a Directed Acyclic Graph")
else:
# Find cycles in the graph
try:
cycle = next(nx.simple_cycles(G))
print("Verification failed: Cycle detected in SoA graph")
print(f"Cycle: {cycle}")
except StopIteration:
print("Verification failed: Graph contains cycles but no cycle found")| When implementing Graph-Based Analysis, ensure that the SPARQL query accurately captures the relevant connections for the analysis. Inaccurate queries can lead to incomplete or incorrect graph representations. |
Catapult Example
The context provides a specific example using the Catapult model where a cycle was intentionally inserted into the graph to demonstrate the verification process. In this example, the cycle was detected using NetworkX, as shown in Table 6 of the context:
Scenario Name |
Graph Failure |
C26 |
Cycle Detected |
The cycle was located between "Impact Velocity" and "Pin Height" as shown in Figure 156 of the context.
Related wiki pages
References
Knowledge Graph
Visualize the relationships between Graph-Based Analysis and related concepts