The Estrada index is a well-known spectral invariant with numerous applications in graph theory, chemical graph theory, complex networks, and quantitative structure–property relationship (QSPR) studies. Motivated by the importance of vertex eccen-tricity in characterizing graph structures, this paper introduces a new eccentricity-based Estrada index defined by

EEe(G)=v∈V(G)∑ee(v)The Estrada index is a well-known spectral invariant with numerous applications in graph theory, chemical graph theory, complex networks, and quantitative structure–property relationship (QSPR) studies.

where ε(v) denotes the eccentricity of the vertex v. The proposed index incorporates distance-related information through an exponential weighting scheme and serves as an alternative descriptor of graph structure. Fundamental properties of the index are established, and exact formulae are derived for several standard graph classes, including complete graphs, cycle graphs, wheel graphs, and path graphs. Further-more, the behavior of the index under graph transformations is investigated through total graphs and eccentric graphs, leading to theoretical results and a conjectured re-lationship involving eccentric graph constructions. Numerical examples are provided to demonstrate the effectiveness of the proposed invariant in distinguishing graph structures. Potential applications of the eccentricity-based Estrada index in network analysis, graph theory, and function approximation are also discussed. The results show that the proposed index provides a useful measure for quantifying structural complexity, connectivity, and distance distribution in graphs and complex networks.