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A Network Theory Approach to Assessing Environmental Sustainability in the Cruz Grande Region, Guerrero, Mexico
(MDPI AG, 2025-10-31)
Luis A. Lucrecio
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BOSCH PÉREZ, PAUL JESÚS
;
Edil D. Molina
;
José Luis Rosas-Acevedo
;
José M. Sigarreta
<jats:p>Traditional composite indicators for the study of sustainability often obscure the complex network of relationships among individual indicators, functioning as black boxes that fail to diagnose the underlying structural and functional weaknesses of the system. The objective of this research is to develop and apply a complementary approach grounded in network theory to diagnose and evaluate the structural and functional cohesion of environmental indicator systems. We developed a study that combines the Principal Component Analysis (PCA) method with network theory to comprehensively analyze the indicator system. The core of this contribution is the development of the Mo(G) index, designed to quantify the structural–functional cohesion of an indicator network. This approach is applied to an environmental dataset of 19 indicators for Cruz Grande, Guerrero, Mexico (2010–2023). The results reveal that although the indicator network is relatively dense (d=0.6199), its structural–functional cohesion is low (Mo(G)=520.68), placing the region in the Fair category. This result provides an explanation for the sustained decline of the system, as shown by the PCA-based Regional Environmental Sustainability Index. We conclude that this approach is a complementary tool for diagnosing and evaluating environmental systems, enabling the detection of vulnerabilities that remain invisible to conventional aggregation methods.</jats:p>
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Inequalities on the Generalized ABC Index
(2021)
BOSCH PÉREZ, PAUL JESÚS
;
Edil D. Molina
;
José M. Rodríguez
;
José M. Sigarreta
In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for ABCα improved, when α=1/2, known results on the ABC index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own.
1Scopus© Citations 6
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On the variable inverse sum deg index
(2023)
Edil D. Molina
;
BOSCH PÉREZ, PAUL JESÚS
;
José M. Sigarreta
;
Eva Tourís
Several important topological indices studied in mathematical chemistry are expressed in the following way Puv∈E(G) F(du, dv), where F is a two variable function that satisfies the condition F(x, y) = F(y, x), uv denotes an edge of the graph G and du is the degree of the vertex u. Among them, the variable inverse sum deg index ISDa, with F(du, dv) = 1/(dua + dva), was found to have several applications. In this paper, we solve some problems posed by Vukičević [1], and we characterize graphs with maximum and minimum values of the ISDa index, for a < 0, in the following sets of graphs with n vertices: graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, we performed a QSPR analysis to test the predictive power of this index for some physicochemical properties of polyaromatic hydrocarbons. © 2023 the Author(s), licensee AIMS Press.
8 1Scopus© Citations 2

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