Descripción



Networks represent the topological skeleton of complex systems that are formed by many interactingelements. The understanding of these structures and their patterns of connections is crucial for comprehending the evolutionary, functional, and dynamical processes taking place in these systems. It is well known that, generally, links do not connect nodes regardless of their characteristics. Assortativity is a global metric of a graph that characterizes the nodes?s tendency to link to other nodes of similar (or different) type. Usually, this concept is applied to the degree of a node (i.e. the number of its adjacent nodes). Thus, degree assortativity is the tendency for nodes of high degree (resp. low degree) in a graph to be connected to high degree nodes (resp. to low degree ones). It is commonly quantified by the Pearson correlation coefficient of the degreedegree correlation. In this work we propose an extension of the concept of degree assortativity to one that account for the correlation between the degrees of the nodes and their nearest neighbours in graphs and networks. For this purpose, we consider the twowalks degree of a node as the sum of all the degrees of its adjacent nodes. The twowalks degree assortativity of a graph is then the Pearson correlation coefficient of the twowalks degree  twowalks degree correlation. We found an analytical expression for this new assortative index as a function of contributing subgraphs, and we also proved that there are a few more fragments contributing to the twowalks degree assortativity than to the degree assortativity. This clearly indicates that the new quantity accounts for more structural information than the previous one. We then study all the 261,000 connected graphs with 9 nodes and observe the existence of assortativeassortative and disassortativedisassortative graphs according to degree and twowalks degree, respectively. More surprisingly, we observe a class of graphs which are degree disassortative and twowalks degree assortative. We explain the existence of some of these graphs due to the presence of certain topological features, such as a node of lowdegree connected to highdegree ones. More importantly, we study a series of 49 realworld networks, where we observe the existence of the disassortativeassortative class in several of them. In particular, all biological networks studied here were in this class. We also conclude that no graphs/networks are possible with assortativedisassortative structure.  
Internacional

Si 
Nombre congreso

LANET 2017 
Tipo de participación

960 
Lugar del congreso

Puebla (México) 
Revisores

Si 
ISBN o ISSN


DOI


Fecha inicio congreso

25/09/2017 
Fecha fin congreso

29/09/2017 
Desde la página

71 
Hasta la página

71 
Título de las actas
