From 7b529807b8259e04c90901be0f6fd3c3dd5a64de Mon Sep 17 00:00:00 2001
From: Sergei Tikhomirov <sergey.s.tikhomirov@gmail.com>
Date: Wed, 13 Mar 2024 13:38:55 +0100
Subject: [PATCH] add updated figure for hops

---
 rln-delay-simulations/message_hops.py  |  11 +-
 rln-delay-simulations/message_hops.svg | 850 +++++++++++--------------
 2 files changed, 368 insertions(+), 493 deletions(-)

diff --git a/rln-delay-simulations/message_hops.py b/rln-delay-simulations/message_hops.py
index b4afb7e..2e74ec0 100644
--- a/rln-delay-simulations/message_hops.py
+++ b/rln-delay-simulations/message_hops.py
@@ -12,9 +12,12 @@ N3 = 100000  # number of nodes in the network (3)
 
 def delay_last_hop(n, d, l):
     # multiply by l for latencies
-    return ceil(log(n)/log(d))
+    numerator = log(((n - 1) * (d - 2) / d) + 1)
+    denominator = log(d - 1)
+    return ceil(numerator / denominator)
 
-ds = np.arange(2,15)
+
+ds = np.arange(3,15)
 ls = np.ones(len(ds))*L
 
 # astype(int) is ok since ceil() returns integers
@@ -39,8 +42,8 @@ with plt.style.context(['science', 'ieee']):
     ax2.set(**dict(ylabel='\nBandwidth amplification'))
 
     # Set the limits of the x-axis and y-axis
-    ax1.set_xlim(2, 14)
-    ax1.set_ylim(2, ax1.get_ylim()[1])  # Ensure that the lower limit is 2
+    ax1.set_xlim(3, 14)
+    ax1.set_ylim(3, ax1.get_ylim()[1])  # Ensure that the lower limit is 2
     
     # Set the limits of the second y-axis to match the first y-axis
     ax2.set_ylim(ax1.get_ylim())
diff --git a/rln-delay-simulations/message_hops.svg b/rln-delay-simulations/message_hops.svg
index 2527a06..e18aa64 100644
--- a/rln-delay-simulations/message_hops.svg
+++ b/rln-delay-simulations/message_hops.svg
@@ -6,7 +6,7 @@
   <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
    <cc:Work>
     <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
-    <dc:date>2024-03-05T16:33:36.471747</dc:date>
+    <dc:date>2024-03-13T13:38:23.988327</dc:date>
     <dc:format>image/svg+xml</dc:format>
     <dc:creator>
      <cc:Agent>
@@ -41,66 +41,27 @@ z
     <g id="xtick_1">
      <g id="line2d_1">
       <defs>
-       <path id="m397f511cbe" d="M 0 0 
+       <path id="mec6c3472b4" d="M 0 0 
 L 0 -3 
 " style="stroke: #000000; stroke-width: 0.5"/>
       </defs>
       <g>
-       <use xlink:href="#m397f511cbe" x="34.409081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mec6c3472b4" x="51.149081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_2">
       <defs>
-       <path id="mf22900d0eb" d="M 0 0 
+       <path id="mc27b083a04" d="M 0 0 
 L 0 3 
 " style="stroke: #000000; stroke-width: 0.5"/>
       </defs>
       <g>
-       <use xlink:href="#mf22900d0eb" x="34.409081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mc27b083a04" x="51.149081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="text_1">
-      <!-- $\mathdefault{2}$ -->
-      <g transform="translate(32.416553 173.439871) scale(0.08 -0.08)">
-       <defs>
-        <path id="NimbusRomNo9L-Regu-32" d="M 3040 875 
-L 2957 907 
-C 2720 544 2637 486 2349 486 
-L 819 486 
-L 1894 1609 
-C 2464 2202 2714 2687 2714 3185 
-C 2714 3823 2195 4313 1530 4313 
-C 1178 4313 845 4173 608 3918 
-C 403 3700 307 3496 198 3043 
-L 333 3011 
-C 589 3636 819 3840 1261 3840 
-C 1798 3840 2163 3476 2163 2940 
-C 2163 2443 1869 1850 1331 1282 
-L 192 77 
-L 192 0 
-L 2688 0 
-L 3040 875 
-z
-" transform="scale(0.015625)"/>
-       </defs>
-       <use xlink:href="#NimbusRomNo9L-Regu-32" transform="scale(0.996264)"/>
-      </g>
-     </g>
-    </g>
-    <g id="xtick_2">
-     <g id="line2d_3">
-      <g>
-       <use xlink:href="#m397f511cbe" x="65.099081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-     <g id="line2d_4">
-      <g>
-       <use xlink:href="#mf22900d0eb" x="65.099081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-     <g id="text_2">
       <!-- $\mathdefault{4}$ -->
-      <g transform="translate(63.106553 173.439871) scale(0.08 -0.08)">
+      <g transform="translate(49.156553 173.439871) scale(0.08 -0.08)">
        <defs>
         <path id="NimbusRomNo9L-Regu-34" d="M 3021 1497 
 L 2368 1497 
@@ -126,20 +87,20 @@ z
       </g>
      </g>
     </g>
-    <g id="xtick_3">
-     <g id="line2d_5">
+    <g id="xtick_2">
+     <g id="line2d_3">
       <g>
-       <use xlink:href="#m397f511cbe" x="95.789081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mec6c3472b4" x="84.629081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="line2d_6">
+     <g id="line2d_4">
       <g>
-       <use xlink:href="#mf22900d0eb" x="95.789081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mc27b083a04" x="84.629081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_3">
+     <g id="text_2">
       <!-- $\mathdefault{6}$ -->
-      <g transform="translate(93.796553 173.439871) scale(0.08 -0.08)">
+      <g transform="translate(82.636553 173.439871) scale(0.08 -0.08)">
        <defs>
         <path id="NimbusRomNo9L-Regu-36" d="M 2854 4391 
 C 2125 4327 1754 4205 1286 3879 
@@ -165,20 +126,20 @@ z
       </g>
      </g>
     </g>
-    <g id="xtick_4">
-     <g id="line2d_7">
+    <g id="xtick_3">
+     <g id="line2d_5">
       <g>
-       <use xlink:href="#m397f511cbe" x="126.479081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mec6c3472b4" x="118.109081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="line2d_8">
+     <g id="line2d_6">
       <g>
-       <use xlink:href="#mf22900d0eb" x="126.479081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mc27b083a04" x="118.109081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_4">
+     <g id="text_3">
       <!-- $\mathdefault{8}$ -->
-      <g transform="translate(124.486553 173.439871) scale(0.08 -0.08)">
+      <g transform="translate(116.116553 173.439871) scale(0.08 -0.08)">
        <defs>
         <path id="NimbusRomNo9L-Regu-38" d="M 1856 2400 
 C 2490 2740 2714 3008 2714 3444 
@@ -210,20 +171,20 @@ z
       </g>
      </g>
     </g>
-    <g id="xtick_5">
-     <g id="line2d_9">
+    <g id="xtick_4">
+     <g id="line2d_7">
       <g>
-       <use xlink:href="#m397f511cbe" x="157.169081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mec6c3472b4" x="151.589081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="line2d_10">
+     <g id="line2d_8">
       <g>
-       <use xlink:href="#mf22900d0eb" x="157.169081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mc27b083a04" x="151.589081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_5">
+     <g id="text_4">
       <!-- $\mathdefault{10}$ -->
-      <g transform="translate(153.184025 173.439871) scale(0.08 -0.08)">
+      <g transform="translate(147.604025 173.439871) scale(0.08 -0.08)">
        <defs>
         <path id="NimbusRomNo9L-Regu-31" d="M 1862 4339 
 L 710 3757 
@@ -264,37 +225,58 @@ z
       </g>
      </g>
     </g>
-    <g id="xtick_6">
-     <g id="line2d_11">
+    <g id="xtick_5">
+     <g id="line2d_9">
       <g>
-       <use xlink:href="#m397f511cbe" x="187.859081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mec6c3472b4" x="185.069081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="line2d_12">
+     <g id="line2d_10">
       <g>
-       <use xlink:href="#mf22900d0eb" x="187.859081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mc27b083a04" x="185.069081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_6">
+     <g id="text_5">
       <!-- $\mathdefault{12}$ -->
-      <g transform="translate(183.874025 173.439871) scale(0.08 -0.08)">
+      <g transform="translate(181.084025 173.439871) scale(0.08 -0.08)">
+       <defs>
+        <path id="NimbusRomNo9L-Regu-32" d="M 3040 875 
+L 2957 907 
+C 2720 544 2637 486 2349 486 
+L 819 486 
+L 1894 1609 
+C 2464 2202 2714 2687 2714 3185 
+C 2714 3823 2195 4313 1530 4313 
+C 1178 4313 845 4173 608 3918 
+C 403 3700 307 3496 198 3043 
+L 333 3011 
+C 589 3636 819 3840 1261 3840 
+C 1798 3840 2163 3476 2163 2940 
+C 2163 2443 1869 1850 1331 1282 
+L 192 77 
+L 192 0 
+L 2688 0 
+L 3040 875 
+z
+" transform="scale(0.015625)"/>
+       </defs>
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
        <use xlink:href="#NimbusRomNo9L-Regu-32" transform="translate(49.8132 0) scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="xtick_7">
-     <g id="line2d_13">
+    <g id="xtick_6">
+     <g id="line2d_11">
       <g>
-       <use xlink:href="#m397f511cbe" x="218.549081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mec6c3472b4" x="218.549081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="line2d_14">
+     <g id="line2d_12">
       <g>
-       <use xlink:href="#mf22900d0eb" x="218.549081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mc27b083a04" x="218.549081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_7">
+     <g id="text_6">
       <!-- $\mathdefault{14}$ -->
       <g transform="translate(214.564025 173.439871) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
@@ -302,233 +284,209 @@ z
       </g>
      </g>
     </g>
-    <g id="xtick_8">
-     <g id="line2d_15">
+    <g id="xtick_7">
+     <g id="line2d_13">
       <defs>
-       <path id="m286d5b382d" d="M 0 0 
+       <path id="m9aed4e227c" d="M 0 0 
 L 0 -1.5 
 " style="stroke: #000000; stroke-width: 0.5"/>
       </defs>
       <g>
-       <use xlink:href="#m286d5b382d" x="42.081581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="42.779081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="line2d_16">
+     <g id="line2d_14">
       <defs>
-       <path id="m25c9201e60" d="M 0 0 
+       <path id="m24e0ea8218" d="M 0 0 
 L 0 1.5 
 " style="stroke: #000000; stroke-width: 0.5"/>
       </defs>
       <g>
-       <use xlink:href="#m25c9201e60" x="42.081581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="42.779081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+      </g>
+     </g>
+    </g>
+    <g id="xtick_8">
+     <g id="line2d_15">
+      <g>
+       <use xlink:href="#m9aed4e227c" x="59.519081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+      </g>
+     </g>
+     <g id="line2d_16">
+      <g>
+       <use xlink:href="#m24e0ea8218" x="59.519081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_9">
      <g id="line2d_17">
       <g>
-       <use xlink:href="#m286d5b382d" x="49.754081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="67.889081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_18">
       <g>
-       <use xlink:href="#m25c9201e60" x="49.754081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="67.889081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_10">
      <g id="line2d_19">
       <g>
-       <use xlink:href="#m286d5b382d" x="57.426581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="76.259081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_20">
       <g>
-       <use xlink:href="#m25c9201e60" x="57.426581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="76.259081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_11">
      <g id="line2d_21">
       <g>
-       <use xlink:href="#m286d5b382d" x="72.771581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="92.999081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_22">
       <g>
-       <use xlink:href="#m25c9201e60" x="72.771581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="92.999081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_12">
      <g id="line2d_23">
       <g>
-       <use xlink:href="#m286d5b382d" x="80.444081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="101.369081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_24">
       <g>
-       <use xlink:href="#m25c9201e60" x="80.444081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="101.369081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_13">
      <g id="line2d_25">
       <g>
-       <use xlink:href="#m286d5b382d" x="88.116581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="109.739081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_26">
       <g>
-       <use xlink:href="#m25c9201e60" x="88.116581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="109.739081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_14">
      <g id="line2d_27">
       <g>
-       <use xlink:href="#m286d5b382d" x="103.461581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="126.479081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_28">
       <g>
-       <use xlink:href="#m25c9201e60" x="103.461581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="126.479081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_15">
      <g id="line2d_29">
       <g>
-       <use xlink:href="#m286d5b382d" x="111.134081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="134.849081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_30">
       <g>
-       <use xlink:href="#m25c9201e60" x="111.134081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="134.849081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_16">
      <g id="line2d_31">
       <g>
-       <use xlink:href="#m286d5b382d" x="118.806581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="143.219081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_32">
       <g>
-       <use xlink:href="#m25c9201e60" x="118.806581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="143.219081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_17">
      <g id="line2d_33">
       <g>
-       <use xlink:href="#m286d5b382d" x="134.151581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="159.959081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_34">
       <g>
-       <use xlink:href="#m25c9201e60" x="134.151581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="159.959081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_18">
      <g id="line2d_35">
       <g>
-       <use xlink:href="#m286d5b382d" x="141.824081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="168.329081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_36">
       <g>
-       <use xlink:href="#m25c9201e60" x="141.824081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="168.329081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_19">
      <g id="line2d_37">
       <g>
-       <use xlink:href="#m286d5b382d" x="149.496581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="176.699081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_38">
       <g>
-       <use xlink:href="#m25c9201e60" x="149.496581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="176.699081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_20">
      <g id="line2d_39">
       <g>
-       <use xlink:href="#m286d5b382d" x="164.841581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="193.439081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_40">
       <g>
-       <use xlink:href="#m25c9201e60" x="164.841581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="193.439081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_21">
      <g id="line2d_41">
       <g>
-       <use xlink:href="#m286d5b382d" x="172.514081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="201.809081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_42">
       <g>
-       <use xlink:href="#m25c9201e60" x="172.514081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="201.809081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="xtick_22">
      <g id="line2d_43">
       <g>
-       <use xlink:href="#m286d5b382d" x="180.186581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m9aed4e227c" x="210.179081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
      <g id="line2d_44">
       <g>
-       <use xlink:href="#m25c9201e60" x="180.186581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m24e0ea8218" x="210.179081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
-    <g id="xtick_23">
-     <g id="line2d_45">
-      <g>
-       <use xlink:href="#m286d5b382d" x="195.531581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-     <g id="line2d_46">
-      <g>
-       <use xlink:href="#m25c9201e60" x="195.531581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="xtick_24">
-     <g id="line2d_47">
-      <g>
-       <use xlink:href="#m286d5b382d" x="203.204081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-     <g id="line2d_48">
-      <g>
-       <use xlink:href="#m25c9201e60" x="203.204081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="xtick_25">
-     <g id="line2d_49">
-      <g>
-       <use xlink:href="#m286d5b382d" x="210.876581" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-     <g id="line2d_50">
-      <g>
-       <use xlink:href="#m25c9201e60" x="210.876581" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="text_8">
+    <g id="text_7">
      <!-- Node degree (D) -->
      <g transform="translate(99.763385 184.56899) scale(0.08 -0.08)">
       <defs>
@@ -750,285 +708,244 @@ z
    </g>
    <g id="matplotlib.axis_2">
     <g id="ytick_1">
-     <g id="line2d_51">
+     <g id="line2d_45">
       <defs>
-       <path id="m937b7ebc29" d="M 0 0 
+       <path id="mdd220916cf" d="M 0 0 
 L 3 0 
 " style="stroke: #000000; stroke-width: 0.5"/>
       </defs>
       <g>
-       <use xlink:href="#m937b7ebc29" x="34.409081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mdd220916cf" x="34.409081" y="153.874677" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_9">
-      <!-- $\mathdefault{2}$ -->
-      <g transform="translate(26.924025 167.238043) scale(0.08 -0.08)">
-       <use xlink:href="#NimbusRomNo9L-Regu-32" transform="scale(0.996264)"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_2">
-     <g id="line2d_52">
-      <g>
-       <use xlink:href="#m937b7ebc29" x="34.409081" y="146.056215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-     <g id="text_10">
+     <g id="text_8">
       <!-- $\mathdefault{4}$ -->
-      <g transform="translate(26.924025 148.758043) scale(0.08 -0.08)">
+      <g transform="translate(26.924025 156.576505) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-34" transform="scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_3">
-     <g id="line2d_53">
+    <g id="ytick_2">
+     <g id="line2d_46">
       <g>
-       <use xlink:href="#m937b7ebc29" x="34.409081" y="127.576215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mdd220916cf" x="34.409081" y="132.5516" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_11">
+     <g id="text_9">
       <!-- $\mathdefault{6}$ -->
-      <g transform="translate(26.924025 130.278043) scale(0.08 -0.08)">
+      <g transform="translate(26.924025 135.253428) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-36" transform="scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_4">
-     <g id="line2d_54">
+    <g id="ytick_3">
+     <g id="line2d_47">
       <g>
-       <use xlink:href="#m937b7ebc29" x="34.409081" y="109.096215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mdd220916cf" x="34.409081" y="111.228523" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_12">
+     <g id="text_10">
       <!-- $\mathdefault{8}$ -->
-      <g transform="translate(26.924025 111.798043) scale(0.08 -0.08)">
+      <g transform="translate(26.924025 113.930351) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-38" transform="scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_5">
-     <g id="line2d_55">
+    <g id="ytick_4">
+     <g id="line2d_48">
       <g>
-       <use xlink:href="#m937b7ebc29" x="34.409081" y="90.616215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mdd220916cf" x="34.409081" y="89.905446" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_13">
+     <g id="text_11">
       <!-- $\mathdefault{10}$ -->
-      <g transform="translate(22.938969 93.318043) scale(0.08 -0.08)">
+      <g transform="translate(22.938969 92.607274) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
        <use xlink:href="#NimbusRomNo9L-Regu-30" transform="translate(49.8132 0) scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_6">
-     <g id="line2d_56">
+    <g id="ytick_5">
+     <g id="line2d_49">
       <g>
-       <use xlink:href="#m937b7ebc29" x="34.409081" y="72.136215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mdd220916cf" x="34.409081" y="68.582369" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_14">
+     <g id="text_12">
       <!-- $\mathdefault{12}$ -->
-      <g transform="translate(22.938969 74.838043) scale(0.08 -0.08)">
+      <g transform="translate(22.938969 71.284197) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
        <use xlink:href="#NimbusRomNo9L-Regu-32" transform="translate(49.8132 0) scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_7">
-     <g id="line2d_57">
+    <g id="ytick_6">
+     <g id="line2d_50">
       <g>
-       <use xlink:href="#m937b7ebc29" x="34.409081" y="53.656215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mdd220916cf" x="34.409081" y="47.259292" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_15">
+     <g id="text_13">
       <!-- $\mathdefault{14}$ -->
-      <g transform="translate(22.938969 56.358043) scale(0.08 -0.08)">
+      <g transform="translate(22.938969 49.96112) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
        <use xlink:href="#NimbusRomNo9L-Regu-34" transform="translate(49.8132 0) scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_8">
-     <g id="line2d_58">
+    <g id="ytick_7">
+     <g id="line2d_51">
       <g>
-       <use xlink:href="#m937b7ebc29" x="34.409081" y="35.176215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#mdd220916cf" x="34.409081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_16">
+     <g id="text_14">
       <!-- $\mathdefault{16}$ -->
-      <g transform="translate(22.938969 37.878043) scale(0.08 -0.08)">
+      <g transform="translate(22.938969 28.638043) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
        <use xlink:href="#NimbusRomNo9L-Regu-36" transform="translate(49.8132 0) scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_9">
-     <g id="line2d_59">
+    <g id="ytick_8">
+     <g id="line2d_52">
       <defs>
-       <path id="mbb0a6ec108" d="M 0 0 
+       <path id="m441963109c" d="M 0 0 
 L 1.5 0 
 " style="stroke: #000000; stroke-width: 0.5"/>
       </defs>
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="159.916215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="159.205446" style="stroke: #000000; stroke-width: 0.5"/>
+      </g>
+     </g>
+    </g>
+    <g id="ytick_9">
+     <g id="line2d_53">
+      <g>
+       <use xlink:href="#m441963109c" x="34.409081" y="148.543908" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_10">
-     <g id="line2d_60">
+     <g id="line2d_54">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="155.296215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="143.213138" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_11">
-     <g id="line2d_61">
+     <g id="line2d_55">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="150.676215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="137.882369" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_12">
-     <g id="line2d_62">
+     <g id="line2d_56">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="141.436215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="127.220831" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_13">
-     <g id="line2d_63">
+     <g id="line2d_57">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="136.816215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="121.890062" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_14">
-     <g id="line2d_64">
+     <g id="line2d_58">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="132.196215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="116.559292" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_15">
-     <g id="line2d_65">
+     <g id="line2d_59">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="122.956215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="105.897754" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_16">
-     <g id="line2d_66">
+     <g id="line2d_60">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="118.336215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="100.566985" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_17">
-     <g id="line2d_67">
+     <g id="line2d_61">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="113.716215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="95.236215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_18">
-     <g id="line2d_68">
+     <g id="line2d_62">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="104.476215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="84.574677" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_19">
-     <g id="line2d_69">
+     <g id="line2d_63">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="99.856215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="79.243908" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_20">
-     <g id="line2d_70">
+     <g id="line2d_64">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="95.236215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="73.913138" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_21">
-     <g id="line2d_71">
+     <g id="line2d_65">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="85.996215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="63.2516" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_22">
-     <g id="line2d_72">
+     <g id="line2d_66">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="81.376215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="57.920831" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_23">
-     <g id="line2d_73">
+     <g id="line2d_67">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="76.756215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="52.590062" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_24">
-     <g id="line2d_74">
+     <g id="line2d_68">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="67.516215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="41.928523" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_25">
-     <g id="line2d_75">
+     <g id="line2d_69">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="62.896215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="36.597754" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_26">
-     <g id="line2d_76">
+     <g id="line2d_70">
       <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="58.276215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#m441963109c" x="34.409081" y="31.266985" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
-    <g id="ytick_27">
-     <g id="line2d_77">
-      <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="49.036215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_28">
-     <g id="line2d_78">
-      <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="44.416215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_29">
-     <g id="line2d_79">
-      <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="39.796215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_30">
-     <g id="line2d_80">
-      <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="30.556215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_31">
-     <g id="line2d_81">
-      <g>
-       <use xlink:href="#mbb0a6ec108" x="34.409081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="text_17">
+    <g id="text_15">
      <!-- Maximum number of hops ($h_{max}$) -->
      <g transform="translate(9.003656 148.7322) rotate(-90) scale(0.08 -0.08)">
       <defs>
@@ -1532,53 +1449,50 @@ z
      <g transform="translate(17.213506 95.236215) rotate(-90) scale(0.08 -0.08)"/>
     </g>
    </g>
-   <g id="line2d_82">
-    <path d="M 34.409081 90.616215 
-L 49.754081 118.336215 
-L 65.099081 136.816215 
-L 80.444081 136.816215 
-L 95.789081 146.056215 
-L 111.134081 146.056215 
-L 126.479081 146.056215 
-L 141.824081 146.056215 
-L 157.169081 155.296215 
-L 172.514081 155.296215 
-L 187.859081 155.296215 
-L 203.204081 155.296215 
-L 218.549081 155.296215 
-" clip-path="url(#p04e0213dc4)" style="fill: none; stroke: #ff0000; stroke-linecap: square"/>
+   <g id="line2d_71">
+    <path d="M 34.409081 100.566985 
+L 51.149081 132.5516 
+L 67.889081 143.213138 
+L 84.629081 143.213138 
+L 101.369081 153.874677 
+L 118.109081 153.874677 
+L 134.849081 153.874677 
+L 151.589081 153.874677 
+L 168.329081 164.536215 
+L 185.069081 164.536215 
+L 201.809081 164.536215 
+L 218.549081 164.536215 
+" clip-path="url(#p7071456e51)" style="fill: none; stroke: #ff0000; stroke-linecap: square"/>
    </g>
-   <g id="line2d_83">
-    <path d="M 34.409081 53.656215 
-L 49.754081 99.856215 
-L 65.099081 118.336215 
-L 80.444081 127.576215 
-L 95.789081 127.576215 
-L 111.134081 136.816215 
-L 126.479081 136.816215 
-L 141.824081 136.816215 
-L 157.169081 146.056215 
-L 172.514081 146.056215 
-L 187.859081 146.056215 
-L 203.204081 146.056215 
-L 218.549081 146.056215 
-" clip-path="url(#p04e0213dc4)" style="fill: none; stroke-dasharray: 3.7,1.6; stroke-dashoffset: 0; stroke: #008000"/>
+   <g id="line2d_72">
+    <path d="M 34.409081 68.582369 
+L 51.149081 111.228523 
+L 67.889081 121.890062 
+L 84.629081 132.5516 
+L 101.369081 143.213138 
+L 118.109081 143.213138 
+L 134.849081 143.213138 
+L 151.589081 143.213138 
+L 168.329081 153.874677 
+L 185.069081 153.874677 
+L 201.809081 153.874677 
+L 218.549081 153.874677 
+" clip-path="url(#p7071456e51)" style="fill: none; stroke-dasharray: 3.7,1.6; stroke-dashoffset: 0; stroke: #008000"/>
    </g>
-   <g id="line2d_84">
+   <g id="line2d_73">
     <path d="M 34.409081 25.936215 
-L 49.754081 81.376215 
-L 65.099081 99.856215 
-L 80.444081 109.096215 
-L 95.789081 118.336215 
-L 111.134081 127.576215 
-L 126.479081 127.576215 
-L 141.824081 127.576215 
-L 157.169081 136.816215 
-L 172.514081 136.816215 
-L 187.859081 136.816215 
-L 203.204081 136.816215 
-L 218.549081 136.816215 
-" clip-path="url(#p04e0213dc4)" style="fill: none; stroke-dasharray: 1,1.65; stroke-dashoffset: 0; stroke: #0000ff"/>
+L 51.149081 89.905446 
+L 67.889081 111.228523 
+L 84.629081 121.890062 
+L 101.369081 121.890062 
+L 118.109081 132.5516 
+L 134.849081 132.5516 
+L 151.589081 132.5516 
+L 168.329081 143.213138 
+L 185.069081 143.213138 
+L 201.809081 143.213138 
+L 218.549081 143.213138 
+" clip-path="url(#p7071456e51)" style="fill: none; stroke-dasharray: 1,1.65; stroke-dashoffset: 0; stroke: #0000ff"/>
    </g>
    <g id="patch_3">
     <path d="M 34.409081 164.536215 
@@ -1600,7 +1514,7 @@ L 218.549081 164.536215
 L 218.549081 25.936215 
 " style="fill: none; stroke: #000000; stroke-width: 0.5; stroke-linejoin: miter; stroke-linecap: square"/>
    </g>
-   <g id="text_18">
+   <g id="text_16">
     <!-- $h_{max}$ and bandwidth amplification depending on node degree $D$ -->
     <g transform="translate(5.908904 10.084396) scale(0.096 -0.096)">
      <defs>
@@ -1806,13 +1720,13 @@ z
     <g transform="translate(126.479081 19.936215) scale(0.096 -0.096)"/>
    </g>
    <g id="legend_1">
-    <g id="line2d_85">
+    <g id="line2d_74">
      <path d="M 52.340281 37.139826 
 L 60.340281 37.139826 
 L 68.340281 37.139826 
 " style="fill: none; stroke: #ff0000; stroke-linecap: square"/>
     </g>
-    <g id="text_19">
+    <g id="text_17">
      <!-- 1000 nodes -->
      <g transform="translate(74.740281 39.939826) scale(0.08 -0.08)">
       <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
@@ -1826,13 +1740,13 @@ L 68.340281 37.139826
       <use xlink:href="#NimbusRomNo9L-Regu-73" transform="translate(417.832572 0) scale(0.996264)"/>
      </g>
     </g>
-    <g id="line2d_86">
+    <g id="line2d_75">
      <path d="M 52.340281 48.465289 
 L 60.340281 48.465289 
 L 68.340281 48.465289 
 " style="fill: none; stroke-dasharray: 3.7,1.6; stroke-dashoffset: 0; stroke: #008000"/>
     </g>
-    <g id="text_20">
+    <g id="text_18">
      <!-- 10000 nodes -->
      <g transform="translate(74.740281 51.265289) scale(0.08 -0.08)">
       <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
@@ -1847,13 +1761,13 @@ L 68.340281 48.465289
       <use xlink:href="#NimbusRomNo9L-Regu-73" transform="translate(467.645773 0) scale(0.996264)"/>
      </g>
     </g>
-    <g id="line2d_87">
+    <g id="line2d_76">
      <path d="M 52.340281 59.790752 
 L 60.340281 59.790752 
 L 68.340281 59.790752 
 " style="fill: none; stroke-dasharray: 1,1.65; stroke-dashoffset: 0; stroke: #0000ff"/>
     </g>
-    <g id="text_21">
+    <g id="text_19">
      <!-- 100000 nodes -->
      <g transform="translate(74.740281 62.590752) scale(0.08 -0.08)">
       <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
@@ -1873,286 +1787,245 @@ L 68.340281 59.790752
   </g>
   <g id="axes_2">
    <g id="matplotlib.axis_3">
-    <g id="ytick_32">
-     <g id="line2d_88">
+    <g id="ytick_27">
+     <g id="line2d_77">
       <defs>
-       <path id="m2433ef40ef" d="M 0 0 
+       <path id="maf88fc6e7f" d="M 0 0 
 L -3 0 
 " style="stroke: #000000; stroke-width: 0.5"/>
       </defs>
       <g>
-       <use xlink:href="#m2433ef40ef" x="218.549081" y="164.536215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#maf88fc6e7f" x="218.549081" y="153.874677" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_22">
-      <!-- $\mathdefault{2}$ -->
-      <g transform="translate(222.049081 167.238043) scale(0.08 -0.08)">
-       <use xlink:href="#NimbusRomNo9L-Regu-32" transform="scale(0.996264)"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_33">
-     <g id="line2d_89">
-      <g>
-       <use xlink:href="#m2433ef40ef" x="218.549081" y="146.056215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-     <g id="text_23">
+     <g id="text_20">
       <!-- $\mathdefault{4}$ -->
-      <g transform="translate(222.049081 148.758043) scale(0.08 -0.08)">
+      <g transform="translate(222.049081 156.576505) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-34" transform="scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_34">
-     <g id="line2d_90">
+    <g id="ytick_28">
+     <g id="line2d_78">
       <g>
-       <use xlink:href="#m2433ef40ef" x="218.549081" y="127.576215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#maf88fc6e7f" x="218.549081" y="132.5516" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_24">
+     <g id="text_21">
       <!-- $\mathdefault{6}$ -->
-      <g transform="translate(222.049081 130.278043) scale(0.08 -0.08)">
+      <g transform="translate(222.049081 135.253428) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-36" transform="scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_35">
-     <g id="line2d_91">
+    <g id="ytick_29">
+     <g id="line2d_79">
       <g>
-       <use xlink:href="#m2433ef40ef" x="218.549081" y="109.096215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#maf88fc6e7f" x="218.549081" y="111.228523" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_25">
+     <g id="text_22">
       <!-- $\mathdefault{8}$ -->
-      <g transform="translate(222.049081 111.798043) scale(0.08 -0.08)">
+      <g transform="translate(222.049081 113.930351) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-38" transform="scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_36">
-     <g id="line2d_92">
+    <g id="ytick_30">
+     <g id="line2d_80">
       <g>
-       <use xlink:href="#m2433ef40ef" x="218.549081" y="90.616215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#maf88fc6e7f" x="218.549081" y="89.905446" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_26">
+     <g id="text_23">
       <!-- $\mathdefault{10}$ -->
-      <g transform="translate(222.049081 93.318043) scale(0.08 -0.08)">
+      <g transform="translate(222.049081 92.607274) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
        <use xlink:href="#NimbusRomNo9L-Regu-30" transform="translate(49.8132 0) scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_37">
-     <g id="line2d_93">
+    <g id="ytick_31">
+     <g id="line2d_81">
       <g>
-       <use xlink:href="#m2433ef40ef" x="218.549081" y="72.136215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#maf88fc6e7f" x="218.549081" y="68.582369" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_27">
+     <g id="text_24">
       <!-- $\mathdefault{12}$ -->
-      <g transform="translate(222.049081 74.838043) scale(0.08 -0.08)">
+      <g transform="translate(222.049081 71.284197) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
        <use xlink:href="#NimbusRomNo9L-Regu-32" transform="translate(49.8132 0) scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_38">
-     <g id="line2d_94">
+    <g id="ytick_32">
+     <g id="line2d_82">
       <g>
-       <use xlink:href="#m2433ef40ef" x="218.549081" y="53.656215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#maf88fc6e7f" x="218.549081" y="47.259292" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_28">
+     <g id="text_25">
       <!-- $\mathdefault{14}$ -->
-      <g transform="translate(222.049081 56.358043) scale(0.08 -0.08)">
+      <g transform="translate(222.049081 49.96112) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
        <use xlink:href="#NimbusRomNo9L-Regu-34" transform="translate(49.8132 0) scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_39">
-     <g id="line2d_95">
+    <g id="ytick_33">
+     <g id="line2d_83">
       <g>
-       <use xlink:href="#m2433ef40ef" x="218.549081" y="35.176215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#maf88fc6e7f" x="218.549081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
-     <g id="text_29">
+     <g id="text_26">
       <!-- $\mathdefault{16}$ -->
-      <g transform="translate(222.049081 37.878043) scale(0.08 -0.08)">
+      <g transform="translate(222.049081 28.638043) scale(0.08 -0.08)">
        <use xlink:href="#NimbusRomNo9L-Regu-31" transform="scale(0.996264)"/>
        <use xlink:href="#NimbusRomNo9L-Regu-36" transform="translate(49.8132 0) scale(0.996264)"/>
       </g>
      </g>
     </g>
-    <g id="ytick_40">
-     <g id="line2d_96">
+    <g id="ytick_34">
+     <g id="line2d_84">
       <defs>
-       <path id="mf8e676e93f" d="M 0 0 
+       <path id="meffacd2acc" d="M 0 0 
 L -1.5 0 
 " style="stroke: #000000; stroke-width: 0.5"/>
       </defs>
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="159.916215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="159.205446" style="stroke: #000000; stroke-width: 0.5"/>
+      </g>
+     </g>
+    </g>
+    <g id="ytick_35">
+     <g id="line2d_85">
+      <g>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="148.543908" style="stroke: #000000; stroke-width: 0.5"/>
+      </g>
+     </g>
+    </g>
+    <g id="ytick_36">
+     <g id="line2d_86">
+      <g>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="143.213138" style="stroke: #000000; stroke-width: 0.5"/>
+      </g>
+     </g>
+    </g>
+    <g id="ytick_37">
+     <g id="line2d_87">
+      <g>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="137.882369" style="stroke: #000000; stroke-width: 0.5"/>
+      </g>
+     </g>
+    </g>
+    <g id="ytick_38">
+     <g id="line2d_88">
+      <g>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="127.220831" style="stroke: #000000; stroke-width: 0.5"/>
+      </g>
+     </g>
+    </g>
+    <g id="ytick_39">
+     <g id="line2d_89">
+      <g>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="121.890062" style="stroke: #000000; stroke-width: 0.5"/>
+      </g>
+     </g>
+    </g>
+    <g id="ytick_40">
+     <g id="line2d_90">
+      <g>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="116.559292" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_41">
-     <g id="line2d_97">
+     <g id="line2d_91">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="155.296215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="105.897754" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_42">
-     <g id="line2d_98">
+     <g id="line2d_92">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="150.676215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="100.566985" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_43">
-     <g id="line2d_99">
+     <g id="line2d_93">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="141.436215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="95.236215" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_44">
-     <g id="line2d_100">
+     <g id="line2d_94">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="136.816215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="84.574677" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_45">
-     <g id="line2d_101">
+     <g id="line2d_95">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="132.196215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="79.243908" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_46">
-     <g id="line2d_102">
+     <g id="line2d_96">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="122.956215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="73.913138" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_47">
-     <g id="line2d_103">
+     <g id="line2d_97">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="118.336215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="63.2516" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_48">
-     <g id="line2d_104">
+     <g id="line2d_98">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="113.716215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="57.920831" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_49">
-     <g id="line2d_105">
+     <g id="line2d_99">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="104.476215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="52.590062" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_50">
-     <g id="line2d_106">
+     <g id="line2d_100">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="99.856215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="41.928523" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_51">
-     <g id="line2d_107">
+     <g id="line2d_101">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="95.236215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="36.597754" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
     <g id="ytick_52">
-     <g id="line2d_108">
+     <g id="line2d_102">
       <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="85.996215" style="stroke: #000000; stroke-width: 0.5"/>
+       <use xlink:href="#meffacd2acc" x="218.549081" y="31.266985" style="stroke: #000000; stroke-width: 0.5"/>
       </g>
      </g>
     </g>
-    <g id="ytick_53">
-     <g id="line2d_109">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="81.376215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_54">
-     <g id="line2d_110">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="76.756215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_55">
-     <g id="line2d_111">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="67.516215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_56">
-     <g id="line2d_112">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="62.896215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_57">
-     <g id="line2d_113">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="58.276215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_58">
-     <g id="line2d_114">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="49.036215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_59">
-     <g id="line2d_115">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="44.416215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_60">
-     <g id="line2d_116">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="39.796215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_61">
-     <g id="line2d_117">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="30.556215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="ytick_62">
-     <g id="line2d_118">
-      <g>
-       <use xlink:href="#mf8e676e93f" x="218.549081" y="25.936215" style="stroke: #000000; stroke-width: 0.5"/>
-      </g>
-     </g>
-    </g>
-    <g id="text_30">
+    <g id="text_27">
      <!--  -->
      <g transform="translate(239.422849 95.236215) rotate(-90) scale(0.08 -0.08)"/>
      <!-- Bandwidth amplification -->
@@ -2216,21 +2089,20 @@ z
      </g>
     </g>
    </g>
-   <g id="line2d_119">
+   <g id="line2d_103">
     <path d="M 34.409081 164.536215 
-L 49.754081 155.296215 
-L 65.099081 146.056215 
-L 80.444081 136.816215 
-L 95.789081 127.576215 
-L 111.134081 118.336215 
-L 126.479081 109.096215 
-L 141.824081 99.856215 
-L 157.169081 90.616215 
-L 172.514081 81.376215 
-L 187.859081 72.136215 
-L 203.204081 62.896215 
-L 218.549081 53.656215 
-" clip-path="url(#p04e0213dc4)" style="fill: none; stroke: #bfbf00; stroke-linecap: square"/>
+L 51.149081 153.874677 
+L 67.889081 143.213138 
+L 84.629081 132.5516 
+L 101.369081 121.890062 
+L 118.109081 111.228523 
+L 134.849081 100.566985 
+L 151.589081 89.905446 
+L 168.329081 79.243908 
+L 185.069081 68.582369 
+L 201.809081 57.920831 
+L 218.549081 47.259292 
+" clip-path="url(#p7071456e51)" style="fill: none; stroke: #bfbf00; stroke-linecap: square"/>
    </g>
    <g id="patch_7">
     <path d="M 34.409081 164.536215 
@@ -2253,13 +2125,13 @@ L 218.549081 25.936215
 " style="fill: none; stroke: #000000; stroke-width: 0.5; stroke-linejoin: miter; stroke-linecap: square"/>
    </g>
    <g id="legend_2">
-    <g id="line2d_120">
+    <g id="line2d_104">
      <path d="M 129.679081 48.232559 
 L 137.679081 48.232559 
 L 145.679081 48.232559 
 " style="fill: none; stroke: #bfbf00; stroke-linecap: square"/>
     </g>
-    <g id="text_31">
+    <g id="text_28">
      <!-- Bandwidth -->
      <g transform="translate(152.079081 46.064902) scale(0.08 -0.08)">
       <use xlink:href="#NimbusRomNo9L-Regu-42" transform="scale(0.996264)"/>
@@ -2292,7 +2164,7 @@ L 145.679081 48.232559
   </g>
  </g>
  <defs>
-  <clipPath id="p04e0213dc4">
+  <clipPath id="p7071456e51">
    <rect x="34.409081" y="25.936215" width="184.14" height="138.6"/>
   </clipPath>
  </defs>