Measuring Complexity at the Requirements Stage: Spectral Metrics as Development Effort Predictors

TL;DR

This work tackles the persistent problem of measuring complexity at the requirements stage by developing spectral structural metrics applied to requirement networks derived via NLP. Through a controlled molecular-integration case study, the authors demonstrate that eigenvalue-based metrics, particularly Graph Energy ($GE$) and Laplacian Graph Energy ($LGE$), predict integration effort with correlations exceeding $r>0.95$, while density-based metrics show no predictive validity. The study establishes a structural isomorphism between molecular graphs and requirement networks, enabling domain-agnostic assessment and suggesting that complexity measured early in RE can forecast downstream integration challenges. The results support a three-stage framework for integrating these metrics into RE workflows and provide a foundation for proactive complexity management, with future work including LLM integration and direct RE validation across industrial contexts.

Abstract

Complexity in engineered systems presents one of the most persistent challenges in modern development since it is driving cost overruns, schedule delays, and outright project failures. Yet while architectural complexity has been studied, the structural complexity embedded within requirements specifications remains poorly understood and inadequately quantified. This gap is consequential: requirements fundamentally drive system design, and complexity introduced at this stage propagates through architecture, implementation, and integration. To address this gap, we build on Natural Language Processing methods that extract structural networks from textual requirements. Using these extracted structures, we conducted a controlled experiment employing molecular integration tasks as structurally isomorphic proxies for requirements integration - leveraging the topological equivalence between molecular graphs and requirement networks while eliminating confounding factors such as domain expertise and semantic ambiguity. Our results demonstrate that spectral measures predict integration effort with correlations exceeding 0.95, while structural metrics achieve correlations above 0.89. Notably, density-based metrics show no significant predictive validity. These findings indicate that eigenvalue-derived measures capture cognitive and effort dimensions that simpler connectivity metrics cannot. As a result, this research bridges a critical methodological gap between architectural complexity analysis and requirements engineering practice, providing a validated foundation for applying these metrics to requirements engineering, where similar structural complexity patterns may predict integration effort.

Figures (3)

• Figure 1: Structural isomorphism between molecular assemblies and requirement specifications. (a) Hierarchical decomposition of requirements mirrors branched molecular structures. (b) Interdependent requirement clusters exhibit cyclic topologies similar to ring-based molecules (e.g., Hexafluoropropene, and 1,3,5-Triazine). (c) Entity-level fragments from NLP extraction (e.g., Requirement 18) map to specific molecular signatures (e.g., Ethanethiol), validating the use of molecular integration tasks as a proxy for requirement complexity .
• Figure 2: Example of completed object assembly
• Figure 3: Box-plot representation of integration times vs. metric values for each metric.