We consider a Leibniz algebra \( \mathfrak L \)=\( \mathfrak I \)⊕\( \mathfrak V \) over an arbitrary base field \( \mathbb F \), being \( \mathfrak I \) the ideal generated by the products [x,x], x∈\( \mathfrak L \). This ideal has a fundamental role in the study presented in our paper. A basis \( B=\{v_i\}_{i \in I} \) of \( \mathfrak L \) is called multiplicative if for any i,j∈\( \mathfrak I \) we have that \( [v_i,v_j]\in\mathbb{F}v_k \) for some k∈I. We associate an adequate graph \( \Gamma({\mathfrak L},B) \) to \( \mathfrak L \) relative to \( B \). By arguing on this graph we show that \( \mathfrak L \) decomposes as a direct sum of ideals, each one being associated to one connected component of \( \Gamma({\mathfrak L},B) \). Also the minimality of \( \mathfrak L \) and the division property of \( \mathfrak L \) are characterized in terms of the weak symmetry of the defined subgraphs \( \Gamma({\mathfrak L},B_{\mathfrak I}) \)  and \( \Gamma({\mathfrak L},B_{\mathfrak V}) \).