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The eccentric connectivity index of the molecular graph \(G\) was proposed by Sharma, Goswami, and Madan in 1997 \cite{17}. This index is defined as \(\xi^c(G) = \sum_{v\in V(G)} \deg(v) \, ec(v)\), where \(\deg(v)\) is the degree of vertex \(v\) in \(G\) and eccentricity \(ec(v)\) is the largest distance between \(v\) and any other vertex of \(G\). Thus, in this paper, we established the general formulas for the eccentric connectivity index of joining a special graph to its paths and of joining two different graphs by a path. Proofs were also provided.