Jamming in complex networks with degree correlation

Abstract

We study the effects of the degree-degree correlations on the pressure congestion J when we apply a dynamical process on scale free complex networks using the gradient network approach. We find that the pressure congestion for disassortative (assortative) networks is lower (bigger) than the one for uncorrelated networks which allow us to affirm that disassortative networks enhance transport through them. This result agree with the fact that many real world transportation networks naturally evolve to this kind of correlation. We explain our results showing that for the disassortative case the clusters in the gradient network turn out to be as much elongated as possible, reducing the pressure congestion J and observing the opposite behavior for the assortative case. Finally we apply our model to real world networks, and the results agree with our theoretical model

Synchronization in scale free networks with degree correlation

“…When r = 0 the network is uncorrelated. As observed in many other works the degree-degree correlation affects considerably the processes that occur on top of them [13][14][15].…”

“…The optimal synchronization found for assortative networks is in our model a topological effect due to the correlations. This is an unexpected result because in many researches it was found that disassortative networks (communication networks) are better for transport [14] and to synchronize oscillators [15]. 0.335 (r min ) (⋄).…”

Assessment of the Resilience of a Complex Network for Crude Oil Transportation on the Maritime Silk Road

“…A disassortative network structure is relatively scattered, core nodes tend to connect with non-core nodes, and there are likely to be more connections in the network, which affects the network's recovery. In this study, the Pearson correlation coefficient method is used to quantify the assortativity of the network by calculating the joint probability distribution of the nodes at both ends of any edge in the network [53]. The formula is as in ( 13):…”

Analysis and perturbation of degree correlation in complex networks

“…In biological and technological networks, high-degree nodes often preferably connect to low-degree nodes, which is referred to as -dissassortative mixing‖. The degree correlation has important influence on the topological properties of networks and may impact related problems on networks such as stability [6], the robustness of networks against attacks [7], the network controllability [8], the traffic dynamics on networks [9,10], the network synchronization [11][12][13], the spreading of information or infections and other dynamic processes [7,[13][14][15][16][17][18][19][20][21][22][23][24].In order to characterize and understand such preference of connections in complex networks, many statistical measures and network models have been introduced and investigated [2,3,[25][26][27][28][29][30][31][32][33][34][35][36]. For example, the average nearest neighbors' degree of nodes (ANND) [3] and the degree correlation coefficient…”