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<p>The system inspired by the biological nervous system, consisting of interconnected neurons, either organic or artificial, is defined as a neural network. In this paper, the investigation of several nondeterministic polynomial-time complete and nondeterministic polynomial-time hard problems on neural networks modeled as graphs has been computed. Specifically, 3-layered and 4-layered Probabilistic Neural Networks (PNNs), Cellular Neural Networks (CNNs), and Tickysym Spiking Neural Networks (TSNNs) has been examined. In order to study there topological properties, we study their structures including the vertex connectivity <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\kappa (G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>κ</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, diameter d(G), edge connectivity <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\lambda (G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, regularity K(G), girth g(G), and vertex cover <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\tau (G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>τ</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> have been computed. These findings provide the network robustness, efficiency, and explainability for topological optimization in neural architectures.</p>

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A Technique for Computing the Topological Structure of Neural Networks Using Graph Theory

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • K. C. Kavitha

摘要

The system inspired by the biological nervous system, consisting of interconnected neurons, either organic or artificial, is defined as a neural network. In this paper, the investigation of several nondeterministic polynomial-time complete and nondeterministic polynomial-time hard problems on neural networks modeled as graphs has been computed. Specifically, 3-layered and 4-layered Probabilistic Neural Networks (PNNs), Cellular Neural Networks (CNNs), and Tickysym Spiking Neural Networks (TSNNs) has been examined. In order to study there topological properties, we study their structures including the vertex connectivity \(\kappa (G)\) κ ( G ) , diameter d(G), edge connectivity \(\lambda (G)\) λ ( G ) , regularity K(G), girth g(G), and vertex cover \(\tau (G)\) τ ( G ) have been computed. These findings provide the network robustness, efficiency, and explainability for topological optimization in neural architectures.