Electrical performance and thermal reliability in conductor systems are strongly influenced by the spatial distribution of current density and resistive losses. Conventional electrical design primarily treats conductor geometry as a mechanical or layout constraint rather than an active parameter influencing current redistribution. This study develops a network-theoretic and biomimetic analytical framework to evaluate how conductor topology affects current distribution, effective resistance, and Joule heating. The proposed framework models closed-loop (“garland”) and hierarchical branched (“leaf-inspired”) conductor geometries as resistive networks represented by weighted graphs. Using Kirchhoff’s laws, equivalent resistance theory, and current density analysis, analytical expressions for current division, power dissipation, and effective resistance are derived. The analysis demonstrates that multi-path conductor topologies reduce peak current density and spatially redistribute Joule heating, thereby improving thermal reliability and fault tolerance without violating fundamental electrical laws. These results align with prior research on loss minimization in electrical and energy systems (Sambaiah & Jayabarathi, 2020; David & Vana, 2025) and thermal optimization in energy infrastructures (Gabbar et al., 2014; Zhao et al., 2021). The framework also extends biomimetic transport optimization principles to electrical conductors, providing a systematic method for designing low-loss, thermally robust conductor networks.