Graph and Network Theory

Estrada, Ernesto

doi:10.1002/3527600434.eap726

Cited by 12 publications

(11 citation statements)

References 69 publications

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“…As more sophisticated models for epidemics on networks, instead of the one presented above, one may use two fundamental models known in the literature: − Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) models, which are extensions of the classical models used in epidemiology that consider the influence of the topology of a network on the propagation of an epidemic, where the spreading of an infectious disease on the network have been modeled representing individuals as nodes and the contacts between them as edges. To better incorporate the dynamical process of the spread of epidemics into the model, one needs to consider a ratio of the infection birth rate and the infection death rate, which is called the epidemic threshold and determines whether an infection becomes epidemic or not. , …”

Section: Resultsmentioning

confidence: 99%

From Infection Clusters to Metal Clusters: Significance of the Lowest Occupied Molecular Orbital (LOMO)

Tsuji

Yoshizawa

2021

ACS Omega

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In this paper, the nature of the lowest-energy electrons is detailed. The orbital occupied by such electrons can be termed the lowest occupied molecular orbital (LOMO). There is a good correspondence between the Huckel method in chemistry and graph theory in mathematics; the molecular orbital, which chemists view as the distribution of an electron with a specific energy, is to mathematicians an algebraic entity, an eigenvector. The mathematical counterpart of LOMO is known as eigenvector centrality, a centrality measure characterizing nodes in networks. It may be instrumental in solving some problems in chemistry, and also it has implications for the challenge facing humanity today. This paper starts with a demonstration of the transmission of infectious disease in social networks, although it is unusual for a chemistry paper but may be a suitable example for understanding what the centrality (LOMO) is all about. The converged distribution of infected patients on the network coincides with the distribution of the LOMO of a molecule that shares the same network structure or topology. This is because the mathematical structures behind graph theory and quantum mechanics are common. Furthermore, the LOMO coefficient can be regarded as a manifestation of the centrality of atoms in an atomic assembly, indicating which atom plays the most important role in the assembly or which one has the greatest influence on the network of these atoms. Therefore, it is proposed that one can predict the binding energy of a metal atom to its cluster based on its LOMO coefficient. A possible improvement of the descriptor using a more sophisticated centrality measure is also discussed.

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Section: Resultsmentioning

confidence: 99%

From Infection Clusters to Metal Clusters: Significance of the Lowest Occupied Molecular Orbital (LOMO)

Tsuji

Yoshizawa

2021

ACS Omega

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“…Borgatti et al 2013;Carrington et al 2005) and for natural sciences such as physics and biology (e.g. Estrada 2013;Ma'ayan 2012). This support is needed to build and share common terminology and tools, and to further develop research methods that respond to the distinctive characteristics of our field.…”

Section: Methodological Challenges and Decision Pointsmentioning

confidence: 99%

Using Network Science to Support Design Research: From Counting to Connecting

Parraguez

Maier

2016

Experimental Design Research

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“…he introduced the concepts of graph theory [11]. It is a prosperous discipline that contains a significant and enormous increase of powerful and massive theorems of wide applicability for representing the data by means of diagrams, matrices or relations in many extensive and popular branches of many fields like computer science, chemistry, science, statistical physics [28], computer science and medicine [12,13,27,30,32].…”

Section: Introductionmentioning

confidence: 99%

Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System

El-Azab¹,

Shokry²,

Aly³

2021

PAMJ

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The incorporation of many various and modern mathematical tools provides efficient and successful methods to model problems with uncertainty such as graph theory, Fuzzy sets, rough sets and soft sets. This powerful incorporation of the three different concepts rough sets, soft sets and graphs is known as soft rough graphs that is introduced previously by Noor et al. The aim of this paper is to propose new concepts of linking soft set, rough set and graph theory in order to create new types of sub-graphs according to properties on the original graph by using generalized relationship through the out-link vertices or directed cycle. Our approach is based on introducing new structure for the roughness of the soft graphs by defining new types of operators by using closed paths. Then, it applies all of these concepts to the cardiovascular system in the human body in order to explain some phenomena and medical facts in a mathematical style. Finally, it discusses the comparison properties and containment relationships between various kinds of new approximation soft subgraph.

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Graph and Network Theory

Cited by 12 publications

References 69 publications

From Infection Clusters to Metal Clusters: Significance of the Lowest Occupied Molecular Orbital (LOMO)

From Infection Clusters to Metal Clusters: Significance of the Lowest Occupied Molecular Orbital (LOMO)

Using Network Science to Support Design Research: From Counting to Connecting

Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System

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