Journal of Advances in Mathematics and Computer Science

Influence maximization (IM) in complex social networks is commonly addressed through stochastic models or local centrality heuristics, such as degree and betweenness centrality. These approaches may not adequately represent the structural reach required to access peripheral regions of a network, particularly when cascade optimization is constrained by a limited seed set. This study proposes a deterministic spectral framework based on the product eccentricity matrix for identifying influential spreaders, referred to as structural heroes, in a graph. The proposed Product Eccentricity Centrality Influence Maximization (PEC-IM) algorithm assigns importance by combining the eccentricities of incident vertices in the construction of a product eccentricity matrix and by deriving node scores from the principal eigenvector associated with this matrix. The method is applied to Zachary’s Karate Club network, which contains 34 nodes and 78 edges, with a density of 0.13904, a diameter of 5, and a radius of 3. The analysis compares the proposed ranking with traditional eigenvector centrality and evaluates the structural discrimination of both approaches using the Gini Coefficient of Centrality. Under the traditional adjacency-based ranking, the initial seed set is {1, 34, 2}, whereas the PEC-IM framework identifies {1, 2, 3} as the optimal seed set for k = 3. The Gini resolution index increases from 0.3245 for traditional eigenvector centrality to 0.4767 for product eccentricity centrality, corresponding to a net structural resolution gain of 46.90%. These findings indicate that the proposed framework provides a deterministic means of ranking nodes by global structural reach while retaining the reported coverage behavior on the selected benchmark network.