Abstract



SelfOrganized Criticality (SOC) is a paradigm of complex system. Empirical examples that have been linked to SOC dynamics are earthquakes, solar flares, neuronal activity, or sand piles among others. Several models have been proposed to determine the physical properties of these dynamics on complex networks. In these models criticality is induced by a ?fitness? parameter defined on the nodes or by a rewiring process. In this work we show a critical network toy model that is driven exclusively by the graph?s topology. Starting from a single node, the network grows by the random addition of a new node (with a single link) at each time step. The criticality appears due to a topological stability condition: A node is stable, if and only if its degree is less than or equal to the average degree of its neighbors plus a global constant (hereafter buffering capacity constant). This local condition is related to an assortative mixing by the average degree of its adjacent nodes, i.e. the nodes tend to link to other nodes (its neighborhood) that show an average property similar to its own. When a node becomes unstable, one of its links is randomly removed and the smallest subnet is deleted. Then the stability condition of the node and its neighbors are checked iteratively until every node in the network is stable. When all the nodes are stable, a new time step starts. Here the set of removals performed until every node in the network is stable represents an avalanche. The size of the avalanche is defined as the total number of nodes removed from the network. The longrange correlations resulting from criticality have been characterized by means of fluctuation analysis and show an anticorrelation in the node?s activity. The distribution plots of the size of avalanches and time intervals between two consecutive events for different values of the buffering capacity constant can be collapsed into universal curves. The probability density function for released energy fluctuations shows the lack of time scales in the correlations. Additionally, the simplicity of the model allows us to study it analytically in the simplest case of linear chains, by means of the Markov chains. This statistical approach and the numerical simulations are in complete agreement. Finally, we have characterized the assortative mixing by vertex degree and the neighborhood?s assortativity. The assortative mixing by vertex degree is null for this model as for ErdösRényi (ER) or the BarabásiAlbert (BA) models. However, assortative mixing by neighborhood?s average degree is significantly positive, while it is null for ER or BA models. We have found that some real networks exhibit positive neigborhood assortativity and null degree assortativity.  
International

Si 
Congress

1st Latin American Conference on Complex Networks (LANET2017) [www.lanetconference.org/lanet2017/index.html] 

960 
Place

Puebla (México) 
Reviewers

Si 
ISBN/ISSN

CDP08UPM 


Start Date

25/09/2017 
End Date

29/09/2017 
From page

143 
To page

143 

LANET 2017  1st Latin American Conference on Complex Networks  Applications to social, biological, and technological systems [www.lanetconference.org/lanet2017/book_abstracts.pdf] 