723 research outputs found
Jamming in complex networks with degree correlation
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
Average nearest neighbor degrees in scale-free networks
The average nearest neighbor degree (ANND) of a node of degree is widely
used to measure dependencies between degrees of neighbor nodes in a network. We
formally analyze ANND in undirected random graphs when the graph size tends to
infinity. The limiting behavior of ANND depends on the variance of the degree
distribution. When the variance is finite, the ANND has a deterministic limit.
When the variance is infinite, the ANND scales with the size of the graph, and
we prove a corresponding central limit theorem in the configuration model (CM,
a network with random connections). As ANND proved uninformative in the
infinite variance scenario, we propose an alternative measure, the average
nearest neighbor rank (ANNR). We prove that ANNR converges to a deterministic
function whenever the degree distribution has finite mean. We then consider the
erased configuration model (ECM), where self-loops and multiple edges are
removed, and investigate the well-known `structural negative correlations', or
`finite-size effects', that arise in simple graphs, such as ECM, because large
nodes can only have a limited number of large neighbors. Interestingly, we
prove that for any fixed , ANNR in ECM converges to the same limit as in CM.
However, numerical experiments show that finite-size effects occur when
scales with
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