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STRUCTURAL AND ANALYTICAL PROPERTIES OF PROBABILITY MEASURES INDUCED BY GRAPHS.

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Title: STRUCTURAL AND ANALYTICAL PROPERTIES OF PROBABILITY MEASURES INDUCED BY GRAPHS.
Authors: Artes Jr., Rosalio G.1 rosalioartes@msutawi-tawi.edu.ph, Sappayani, Arsanial E.2 arsappayanial@gmail.com, Kiram, Myrna S.2 myrnasungak@gmail.com, Rasid, Sherna A.3 shernrasid@gmail.com
Source: Advances & Applications in Discrete Mathematics. May2026, Vol. 43 Issue 4, p483-495. 13p.
Subjects: Probability measures, Graph theory, Entropy, Matching theory
Abstract: This paper extends the concept of probability measures induced by graphs by developing a comprehensive structural and analytical framework for probable graphs. A graph-induced probability measure is defined via normalized vertex degrees. It is shown that a graph is probable if and only if its size equals half its order, establishing a direct connection between probabilistic normalization and graph structure. New results include a characterization of probable graphs via average degree, connections with perfect matchings, entropy-based interpretations, and the introduction of a probability generating polynomial. These results provide a deeper understanding of the interplay between graph theory and probability, and open new directions for applications in network analysis and stochastic modeling. [ABSTRACT FROM AUTHOR]
Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: STRUCTURAL AND ANALYTICAL PROPERTIES OF PROBABILITY MEASURES INDUCED BY GRAPHS.
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  Data: <searchLink fieldCode="JN" term="%22Advances+%26+Applications+in+Discrete+Mathematics%22">Advances & Applications in Discrete Mathematics</searchLink>. May2026, Vol. 43 Issue 4, p483-495. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Probability+measures%22">Probability measures</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Entropy%22">Entropy</searchLink><br /><searchLink fieldCode="DE" term="%22Matching+theory%22">Matching theory</searchLink>
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  Data: This paper extends the concept of probability measures induced by graphs by developing a comprehensive structural and analytical framework for probable graphs. A graph-induced probability measure is defined via normalized vertex degrees. It is shown that a graph is probable if and only if its size equals half its order, establishing a direct connection between probabilistic normalization and graph structure. New results include a characterization of probable graphs via average degree, connections with perfect matchings, entropy-based interpretations, and the introduction of a probability generating polynomial. These results provide a deeper understanding of the interplay between graph theory and probability, and open new directions for applications in network analysis and stochastic modeling. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Entropy
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              M: 05
              Text: May2026
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              Y: 2026
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