Establishing a node importance ranking is a problem that has attracted the attention of many researchers in recent decades. For unweighted networks where the edges do not have any attached weight, many proposals have been presented, considering local or global information of the networks. On the contrary, it occurs in undirected edge-weighted networks, where the proposals to address this problem have been more scarce. In this paper, a ranking method of node importance for undirected and edge-weighted is provided, generalizing the measure of line importance (DIL) based on the centrality degree proposed by Opsahl. The experimentation was done on five real networks and the results illustrate the benefits of our proposal.

The understanding of infectious diseases is a priority in the field of public health. This has generated the inclusion of several disciplines and tools that allow for analyzing the dissemination of infectious diseases. The aim of this manuscript is to model the spreading of a disease in a population that is registered in a database. From this database, we obtain an edge-weighted graph. The spreading was modeled with the classic SIR model. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics. Moreover, a deterministic approximation is provided. With database COVID-19 from a city in Chile, we analyzed our model with relationship variables between people. We obtained a graph with 3866 vertices and 6,841,470 edges. We fitted the curve of the real data and we have done some simulations on the obtained graph. Our model is adjusted to the spread of the disease. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics, in this case with real data of COVID-19. This valuable information allows us to also include/understand the networks of dissemination of epidemics diseases as well as the implementation of preventive measures of public health. These findings are important in COVID-19’s pandemic context.

Fake news, viruses on computer systems or infectious diseases on communities are some of the problems that are addressed by researchers dedicated to study complex networks. The immunization process is the solution to these challenges and hence the importance of obtaining immunization strategies that control these spreads. In this paper, we evaluate the effectiveness of the DIL-Wα ranking in the immunization of nodes that are attacked by an infectious disease that spreads on an edge-weighted graph using a graph-based SIR model. The experimentation was done on real and scale-free networks and the results illustrate the benefits of this ranking.

Among the diverse and important applications that networks currently have is the modeling of infectious diseases. Immunization, or the process of protecting nodes in the network, plays a key role in stopping diseases from spreading. Hence the importance of having tools or strategies that allow the solving of this challenge. In this paper, we evaluate the effectiveness of the DIL-Wα ranking in immunizing nodes in an edge-weighted network with 3866 nodes and 6,841,470 edges. The network is obtained from a real database and the spread of COVID-19 was modeled with the classic SIR model. We apply the protection to the network, according to the importance ranking list produced by DIL-Wα, considering different protection budgets. Furthermore, we consider three different values for α; in this way, we compare how the protection performs according to the value of α.

En este artículo proponemos una herramienta para analizar la bibliografía que está construido con tres hebras, la primera es filosófica, donde utilizamos el concepto de rizoma (Deleuze y Guattari, 1980) para acercarnos a la creciente literatura que se está produciendo en el mundo. La segunda es matemática, utilizaremos la teoría de grafos para construir el Espacio Rizomático Conceptual. La tercera y última hebra de este trabajo es informática, utilizaremos herramientas de ciencias de datos para operacionalizar estas ideas. Estas hebras nos permitirán construir rizomas conceptuales a partir de artículos de investigación científica. También, mostramos algunos potenciales usos con bases específicas, proponiendo además una interpretación de los mismos utilizando herramientas propias de la teoría de grafos y también, mediante los conceptos de diferencia y repetición de Deleuze (2002). Por último, definimos los conceptos de isla rizomática, periferia visible e invisible y ego rizomático, todos estos conceptos nos permiten analizar de forma global un corpus bibliográfico.