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diff --git a/_images/e86d6caf36a3d61015095ef2e930b5a6c4fd8307911f620e7c3a6b0207d1dccf.png b/_images/e86d6caf36a3d61015095ef2e930b5a6c4fd8307911f620e7c3a6b0207d1dccf.png
diff --git a/notebooks/cryptography.html b/notebooks/cryptography.html
@@ -579,22 +579,22 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
         white-space: pre-wrap;
     }
   </style>
-  </div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Znxqejy 1
+  </div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Buwtsfh 1
 
 
-Dgy Sxwejy Jwwgke, ki Ljwwatzn Nxww, gt Dkvjydjedngyj, sxd x vxt snk,
-iky ngd kst xvhdjvjte, tjbjy ekkl hq xta rkkl rhe enj Rxyktjexmj;
-enjyj nj ikhtc kzzhqxegkt iky xt gcwj nkhy, xtc zktdkwxegkt gt x
-cgdeyjddjc ktj; enjyj ngd ixzhwegjd sjyj ykhdjc gtek xcvgyxegkt xtc
-yjdqjze, ra zktejvqwxegtm enj wgvgejc yjvtxte ki enj jxywgjde qxejted;
-enjyj xta htsjwzkvj djtdxegktd, xygdgtm iykv ckvjdegz xiixgyd
-znxtmjc txehyxwwa gtek qgea xtc zktejvqe xd nj ehytjc kbjy
-enj xwvkde jtcwjdd zyjxegktd ki enj wxde zjtehya; xtc enjyj,
-gi jbjya kenjy wjxi sjyj qksjywjdd, nj zkhwc yjxc ngd kst ngdekya
-sgen xt gtejyjde sngzn tjbjy ixgwjc.  Engd sxd enj qxmj xe sngzn
-enj ixbkhygej bkwhvj xwsxad kqjtjc:
+Gmh Lwvsfh Fvvmcs, cx Dfvvojbu Uwvv, mj Gckfhgfsgumhf, lwg w kwj luc,
+xch umg clj wkygfkfjs, jfrfh sccd yt wjo qccd qys suf Qwhcjfswif;
+sufhf uf xcyjz cbbytwsmcj xch wj mzvf ucyh, wjz bcjgcvwsmcj mj w
+zmgshfggfz cjf; sufhf umg xwbyvsmfg lfhf hcygfz mjsc wzkmhwsmcj wjz
+hfgtfbs, qo bcjsfktvwsmji suf vmkmsfz hfkjwjs cx suf fwhvmfgs twsfjsg;
+sufhf wjo yjlfvbckf gfjgwsmcjg, whmgmji xhck zckfgsmb wxxwmhg
+buwjifz jwsyhwvvo mjsc tmso wjz bcjsfkts wg uf syhjfz crfh
+suf wvkcgs fjzvfgg bhfwsmcjg cx suf vwgs bfjsyho; wjz sufhf,
+mx frfho csufh vfwx lfhf tclfhvfgg, uf bcyvz hfwz umg clj umgscho
+lmsu wj mjsfhfgs lumbu jfrfh xwmvfz.  Sumg lwg suf twif ws lumbu
+suf xwrcyhmsf rcvykf wvlwog ctfjfz:
 
-           &quot;JWWGKE KI LJWWATZN NXWW.
+           &quot;FVVMCS CX DFVVOJBU UWVV.
 
 &quot;
 </pre></div>
@@ -661,8 +661,8 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
         white-space: pre-wrap;
     }
   </style>
-  </div><img alt="../_images/83fa9d4bfa53ec406c65e98357e952724817ced2f5fddd8f72b8d88ca21588d6.png" src="../_images/83fa9d4bfa53ec406c65e98357e952724817ced2f5fddd8f72b8d88ca21588d6.png" />
-<img alt="../_images/84697fb5df5428ad73bdba0e0298ada6f641170fd23e38d28177ed65ec293f86.png" src="../_images/84697fb5df5428ad73bdba0e0298ada6f641170fd23e38d28177ed65ec293f86.png" />
+  </div><img alt="../_images/0eedafd48be3cf1ffdf359b7128c0ef150d6d62f02ec01f867d4570c4586566c.png" src="../_images/0eedafd48be3cf1ffdf359b7128c0ef150d6d62f02ec01f867d4570c4586566c.png" />
+<img alt="../_images/06b0e64495e11b35d0607e10672e296106bb2410318b18ca83ed9fdb459b1f47.png" src="../_images/06b0e64495e11b35d0607e10672e296106bb2410318b18ca83ed9fdb459b1f47.png" />
 </div>
 </div>
 <p>As the above distribution shows us, even though each individual letter in the encrypted text no longer has the same occurance probability as it does in typical English text, the general shape of the re-ordered distribution is still the same. We can use this to build a first-pass remapping to attempt deciphering the encrypted text, substituting each encrypted letter with the English letter closest in usage frequency.</p>
@@ -823,7 +823,7 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
         white-space: pre-wrap;
     }
   </style>
-  </div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap N and T 	percent valid English words: 0.5160721105097512 
+  </div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap U and J 	percent valid English words: 0.5160721105097512 
 
 
 Fhabter 1
@@ -846,7 +846,7 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
 &quot;
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap C and W 	percent valid English words: 0.6301505155453719 
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap Z and V 	percent valid English words: 0.6301505155453719 
 
 
 Fhabter 1
@@ -869,53 +869,30 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
 &quot;
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap R and Q 	percent valid English words: 0.6855502442750102 
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap B and X 	percent valid English words: 0.7351821857016816 
 
 
-Fhapter 1
-
-
-Sir Walter Elliot, oc Kellynfh Hall, in Somersetshire, was a man who,
-cor his own amusement, never took up any book but the Baronetage;
-there he cound offupation cor an idle hour, and fonsolation in a
-distressed one; there his cafulties were roused into admiration and
-respeft, by fontemplating the limited remnant oc the earliest patents;
-there any unwelfome sensations, arising crom domestif accairs
-fhanged naturally into pity and fontempt as he turned over
-the almost endless freations oc the last fentury; and there,
-ic every other leac were powerless, he fould read his own history
-with an interest whifh never cailed.  This was the page at whifh
-the cavourite volume always opened:
-
-           &quot;ELLIOT OC KELLYNFH HALL.
-
-&quot;
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap Z and I 	percent valid English words: 0.8056729743610003 
-
-
-Chapter 1
+Chabter 1
 
 
 Sir Walter Elliot, of Kellynch Hall, in Somersetshire, was a man who,
-for his own amusement, never took up any book but the Baronetage;
-there he found occupation for an idle hour, and consolation in a
+for his own amusement, never took ub any pook put the Paronetage;
+there he found occubation for an idle hour, and consolation in a
 distressed one; there his faculties were roused into admiration and
-respect, by contemplating the limited remnant of the earliest patents;
+resbect, py contemblating the limited remnant of the earliest batents;
 there any unwelcome sensations, arising from domestic affairs
-changed naturally into pity and contempt as he turned over
+changed naturally into bity and contembt as he turned over
 the almost endless creations of the last century; and there,
-if every other leaf were powerless, he could read his own history
-with an interest which never failed.  This was the page at which
-the favourite volume always opened:
+if every other leaf were bowerless, he could read his own history
+with an interest which never failed.  This was the bage at which
+the favourite volume always obened:
 
            &quot;ELLIOT OF KELLYNCH HALL.
 
 &quot;
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap F and P 	percent valid English words: 0.8099658936778203 
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap Q and T 	percent valid English words: 0.8056729743610003 
 
 
 Chapter 1
@@ -938,7 +915,7 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
 &quot;
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap F and U 	percent valid English words: 0.8171690435744479 
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap E and N 	percent valid English words: 0.8100317359986304 
 
 
 Chapter 1

diff --git a/notebooks/markov-properties.html b/notebooks/markov-properties.html
@@ -639,7 +639,7 @@ <h2>Markov Property:<a class="headerlink" href="#markov-property" title="Permali
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/33b5b8500218c0deadd2b3194f23008980bf9d01d580ad7b766f0069cea601e9.png" src="../_images/33b5b8500218c0deadd2b3194f23008980bf9d01d580ad7b766f0069cea601e9.png" />
+<img alt="../_images/001a784c446eedac4310e565bb5afee36ef24f3515b8045f2bdd4f3c093420f7.png" src="../_images/001a784c446eedac4310e565bb5afee36ef24f3515b8045f2bdd4f3c093420f7.png" />
 </div>
 </div>
 <p><br/><big>This holds true for most real-life markov chain models, no matter the size of the model. For example:</big></p>
@@ -671,15 +671,15 @@ <h2>Markov Property:<a class="headerlink" href="#markov-property" title="Permali
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.2528 0.3704 0.3768]
- [0.213  0.2853 0.5017]
- [0.2449 0.4089 0.3462]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.0686 0.2234 0.7079]
+ [0.1632 0.4229 0.414 ]
+ [0.2265 0.7077 0.0658]]
 
-(S1, S1): 0.2528		(S1, S2): 0.3704		(S1, S3): 0.3768		(S2, S1): 0.213		(S2, S2): 0.2853		(S2, S3): 0.5017		(S3, S1): 0.2449		(S3, S2): 0.4089		(S3, S3): 0.3462		
+(S1, S1): 0.0686		(S1, S2): 0.2234		(S1, S3): 0.7079		(S2, S1): 0.1632		(S2, S2): 0.4229		(S2, S3): 0.414		(S3, S1): 0.2265		(S3, S2): 0.7077		(S3, S3): 0.0658		
 </pre></div>
 </div>
-<img alt="../_images/65f31d40206d73379196b02de7050e7d5e1a1a9f08a1440b129974cbc14b3592.png" src="../_images/65f31d40206d73379196b02de7050e7d5e1a1a9f08a1440b129974cbc14b3592.png" />
-<img alt="../_images/61bfaed14d66168c719da2e83337bc291afeee567ab97e81610b4253bf3751fa.png" src="../_images/61bfaed14d66168c719da2e83337bc291afeee567ab97e81610b4253bf3751fa.png" />
+<img alt="../_images/e01f3489391b5b9ef61ac272f1bc7e0925b2a6ce8693a1a36bfdabd63e55fefb.png" src="../_images/e01f3489391b5b9ef61ac272f1bc7e0925b2a6ce8693a1a36bfdabd63e55fefb.png" />
+<img alt="../_images/dd60e879c62cdd2d80da7b98a6a793a3eac6ec3f3144b2dc8cafe632d635c489.png" src="../_images/dd60e879c62cdd2d80da7b98a6a793a3eac6ec3f3144b2dc8cafe632d635c489.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -711,17 +711,17 @@ <h2>Markov Property:<a class="headerlink" href="#markov-property" title="Permali
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.2264 0.27   0.1052 0.1751 0.2233]
- [0.2459 0.1966 0.1791 0.1951 0.1833]
- [0.4235 0.0861 0.451  0.0278 0.0116]
- [0.237  0.1901 0.3617 0.0537 0.1575]
- [0.2628 0.1998 0.2037 0.2042 0.1295]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.248  0.1642 0.2624 0.2632 0.0622]
+ [0.0404 0.1524 0.0644 0.3747 0.3681]
+ [0.2573 0.3681 0.0636 0.1906 0.1205]
+ [0.4714 0.0347 0.3545 0.0625 0.0769]
+ [0.1694 0.0486 0.0535 0.3424 0.3862]]
 
-(S1, S1): 0.2264		(S1, S2): 0.27		(S1, S3): 0.1052		(S1, S4): 0.1751		(S1, S5): 0.2233		(S2, S1): 0.2459		(S2, S2): 0.1966		(S2, S3): 0.1791		(S2, S4): 0.1951		(S2, S5): 0.1833		(S3, S1): 0.4235		(S3, S2): 0.0861		(S3, S3): 0.451		(S3, S4): 0.0278		(S3, S5): 0.0116		(S4, S1): 0.237		(S4, S2): 0.1901		(S4, S3): 0.3617		(S4, S4): 0.0537		(S4, S5): 0.1575		(S5, S1): 0.2628		(S5, S2): 0.1998		(S5, S3): 0.2037		(S5, S4): 0.2042		(S5, S5): 0.1295		
+(S1, S1): 0.248		(S1, S2): 0.1642		(S1, S3): 0.2624		(S1, S4): 0.2632		(S1, S5): 0.0622		(S2, S1): 0.0404		(S2, S2): 0.1524		(S2, S3): 0.0644		(S2, S4): 0.3747		(S2, S5): 0.3681		(S3, S1): 0.2573		(S3, S2): 0.3681		(S3, S3): 0.0636		(S3, S4): 0.1906		(S3, S5): 0.1205		(S4, S1): 0.4714		(S4, S2): 0.0347		(S4, S3): 0.3545		(S4, S4): 0.0625		(S4, S5): 0.0769		(S5, S1): 0.1694		(S5, S2): 0.0486		(S5, S3): 0.0535		(S5, S4): 0.3424		(S5, S5): 0.3862		
 </pre></div>
 </div>
-<img alt="../_images/51fa432679182924440a64ce65028d1df58927ce869c3770c07f33bcf8c73f67.png" src="../_images/51fa432679182924440a64ce65028d1df58927ce869c3770c07f33bcf8c73f67.png" />
-<img alt="../_images/5c64d9ae6d86ff0e56d136ee8efbf11e4f306d6f99fa12a936c821ae487f01e8.png" src="../_images/5c64d9ae6d86ff0e56d136ee8efbf11e4f306d6f99fa12a936c821ae487f01e8.png" />
+<img alt="../_images/d5c7a9caf2153c0f30b4a0e2c0bd8dd97dd8b56900788d13e9c244c9cf49919d.png" src="../_images/d5c7a9caf2153c0f30b4a0e2c0bd8dd97dd8b56900788d13e9c244c9cf49919d.png" />
+<img alt="../_images/30191a731b9e2fb391963ee711567c9bb3730b30ea4c881072c041241adb5a2a.png" src="../_images/30191a731b9e2fb391963ee711567c9bb3730b30ea4c881072c041241adb5a2a.png" />
 </div>
 </div>
 <p><br/>… even size-105 markov chains, but that will require a lot of computational power. So, let’s jump to a different type of markov chains/states…</p>
@@ -759,18 +759,18 @@ <h3>Absorbing Markov Chains and Absorbing States:<a class="headerlink" href="#ab
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[1.     0.     0.    ]
- [0.1283 0.6388 0.2328]
- [0.38   0.3575 0.2624]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.343  0.3319 0.3251]
+ [0.     1.     0.    ]
+ [0.592  0.1755 0.2325]]
 
-(S1, S1): 1.0		(S2, S1): 0.1283		(S2, S2): 0.6388		(S2, S3): 0.2328		(S3, S1): 0.38		(S3, S2): 0.3575		(S3, S3): 0.2624		
+(S1, S1): 0.343		(S1, S2): 0.3319		(S1, S3): 0.3251		(S2, S2): 1.0		(S3, S1): 0.592		(S3, S2): 0.1755		(S3, S3): 0.2325		
 </pre></div>
 </div>
-<img alt="../_images/e86d6caf36a3d61015095ef2e930b5a6c4fd8307911f620e7c3a6b0207d1dccf.png" src="../_images/e86d6caf36a3d61015095ef2e930b5a6c4fd8307911f620e7c3a6b0207d1dccf.png" />
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>That is, S1 is the Absorbing State.
+<img alt="../_images/96c622fed9dbdb97b069b1db43410f11b96da9e5328bd19a5f1ca462c5b221ab.png" src="../_images/96c622fed9dbdb97b069b1db43410f11b96da9e5328bd19a5f1ca462c5b221ab.png" />
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>That is, S2 is the Absorbing State.
 </pre></div>
 </div>
-<img alt="../_images/126bb9f77fb9de8d6138c738075eecb126ffb5d25ad9794c4252cdbc0fdc2873.png" src="../_images/126bb9f77fb9de8d6138c738075eecb126ffb5d25ad9794c4252cdbc0fdc2873.png" />
+<img alt="../_images/721eade9aee70e21d3e29e82660c47d1779f55a1f859616a7ad2e439273ff00c.png" src="../_images/721eade9aee70e21d3e29e82660c47d1779f55a1f859616a7ad2e439273ff00c.png" />
 </div>
 </div>
 <p><br/>Such tranfer matrices have the form of: <span class="math notranslate nohighlight">\(P_{A\ ((m+n)\times(m+n))} = \begin{bmatrix}I_m&amp;O\\R&amp;Q_n\end{bmatrix}\)</span>.</p>

diff --git a/notebooks/network-theory.html b/notebooks/network-theory.html
@@ -495,7 +495,7 @@ <h3>Network Structures and Small-worldness:<a class="headerlink" href="#network-
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-<img alt="../_images/4841a8a216e4fa5efadc5a843f5200d2060015a545db519babcf4758109727f2.png" src="../_images/4841a8a216e4fa5efadc5a843f5200d2060015a545db519babcf4758109727f2.png" />
+<img alt="../_images/4720e75188dcb9ce8a9a439d8590c57974d4eb9671462c120f6c4d1f50a5b745.png" src="../_images/4720e75188dcb9ce8a9a439d8590c57974d4eb9671462c120f6c4d1f50a5b745.png" />
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@@ -569,7 +569,7 @@ <h2>Network Metrics:<a class="headerlink" href="#network-metrics" title="Permali
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+<img alt="../_images/ae145a57ce16fbc3e7a869804e9214f5a23cbfe33e1f0d7db6118f72fa5c0883.png" src="../_images/ae145a57ce16fbc3e7a869804e9214f5a23cbfe33e1f0d7db6118f72fa5c0883.png" />
 </div>
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@@ -647,7 +647,7 @@ <h4>Community Structures – Modularity and Clustering:<a class="headerlink" hre
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-<img alt="../_images/6675134bad87d24c1d036709b3910bdfd36c86db80d0c473d46650c78ce6949e.png" src="../_images/6675134bad87d24c1d036709b3910bdfd36c86db80d0c473d46650c78ce6949e.png" />
+<img alt="../_images/36a254fad87f49a0aba69089920d0e6530956e3784c1bde6d9a50fdd519efe7d.png" src="../_images/36a254fad87f49a0aba69089920d0e6530956e3784c1bde6d9a50fdd519efe7d.png" />
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diff --git a/reports/notebooks/markov-properties.err.log b/reports/notebooks/markov-properties.err.log
@@ -3,7 +3,7 @@ Traceback (most recent call last):
     executenb(
   File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 1305, in execute
     return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute()
-  File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 172, in wrapped
+  File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped
     return loop.run_until_complete(inner)
   File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/asyncio/base_events.py", line 616, in run_until_complete
     return future.result()

diff --git a/searchindex.js b/searchindex.js