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Added link to bmlrp-simple + clickable references
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Anatoliy Zinovyev committed Apr 19, 2016
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%\geometry{letterpaper}

\usepackage[usenames, dvipsnames]{color}
\usepackage{url}
\usepackage[hidelinks]{hyperref}
\usepackage{tikz}

\ifCLASSOPTIONcompsoc
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\subsection{Average node degree}
\label{sec:analysis:nodedegree}

Despite several advantages, BMLRP does not guarantee that the routing table sizes for higher level networks remain low. To analyze this aspect, we implemented and tested Algorithms~\ref{alg:routes} and \ref{alg:connect} on a static network to track the average degree of nodes across each level.
Despite several advantages, BMLRP does not guarantee that the routing table sizes for higher level networks remain low. To analyze this aspect, we implemented\footnote{\url{https://github.com/aszinovyev/bmlrp-simple}} and tested Algorithms~\ref{alg:routes} and \ref{alg:connect} on a static network to track the average degree of nodes across each level.

In Fig.~\ref{fig:degrees}, the black line shows the simulation result on $2^{14}$ identical nodes uniformly distributed in a square area. Note that the average number of neighbors first stabilizes around the value~6 and then continues decreasing as the network level $i$ grows. Additionally, we randomly connected 1\%, 5\% and 10\% nodes in the network independently of their coordinates. The blue, orange and red lines show that when random long-range edges are added, the higher level networks become close world networks and the number of mandatory connections fails to decrease. The impact, however, is small; the red line demonstrates that even when 10\% of the nodes are randomly connected, the average number of level-$i$ neighbors in the network does not exceed 21 for $2^{14}$ nodes.

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