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A STUDY ON ROUGH GRAPHS
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AI
DOI：10.5206/mase/23201.png)
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Abstract
En 中文
Rough graphs have emerged as a significant mathematical tool for modeling imprecise and incomplete information within graph-structured data. By leveraging rough set theory, these structures manage uncertainty through the construction of lower and upper approximations, providing a robust framework for analyzing vague or ambiguous networks. Despite the growing body of literature on rough graphs, a consistent and comprehensive theoretical foundation remains elusive. In this paper, we critically review existing partition-based approaches and identify persisting structural inconsistencies in their foundational definitions, such as the generation of invalid subgraphs and hanging edges. To address these gaps, we propose a unified, topologically consistent framework. Inspired by the theory of rough relations, we generalize vertex-based rough graphs to settings where the vertex set is granulated by a covering rather than a strict partition. Furthermore, we introduce three novel types of edge-based rough graphs derived from coverings of the edge set, demonstrating that our approach inherently preserves subgraph validity. Synthesizing these two perspectives, we propose hybrid rough graph models that establish a comprehensive multi-granulation environment for both the vertex and edge universes. Finally, we illustrate the practical utility of our proposed models through applications in social network analysis and protein-protein interaction (PPI) networks, highlighting their effectiveness in isolating core communities and identifying boundary nodes.
Keywords:
Rough set theory
rough graphs
graph covering
approximation operators
rough relations
Journal
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17
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