[skip ci] docs built of 122fca2

networkx · Aug 7, 2023 · d8a63b4 · d8a63b4
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diff --git a/_sources/content/algorithms/assortativity/correlation.ipynb b/_sources/content/algorithms/assortativity/correlation.ipynb
diff --git a/_sources/content/algorithms/dag/index.ipynb b/_sources/content/algorithms/dag/index.ipynb
diff --git a/_sources/content/algorithms/euler/euler.ipynb b/_sources/content/algorithms/euler/euler.ipynb
diff --git a/_sources/content/algorithms/flow/dinitz_alg.ipynb b/_sources/content/algorithms/flow/dinitz_alg.ipynb
diff --git a/_sources/content/algorithms/isomorphism/isomorphism.ipynb b/_sources/content/algorithms/isomorphism/isomorphism.ipynb
diff --git a/_sources/content/algorithms/lca/LCA.ipynb b/_sources/content/algorithms/lca/LCA.ipynb
diff --git a/_sources/content/exploratory_notebooks/facebook_notebook.ipynb b/_sources/content/exploratory_notebooks/facebook_notebook.ipynb
diff --git a/_sources/content/generators/geometric.ipynb b/_sources/content/generators/geometric.ipynb
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diff --git a/content/algorithms/assortativity/correlation.html b/content/algorithms/assortativity/correlation.html
@@ -598,7 +598,7 @@ <h2>Example<a class="headerlink" href="#example" title="Permalink to this headin
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../../../_images/b464278155088c75a4be5e5748afec9ee07574200976dddbbdd57ed6c60dc3e6.png" src="../../../_images/b464278155088c75a4be5e5748afec9ee07574200976dddbbdd57ed6c60dc3e6.png" />
+<img alt="../../../_images/1db36cb7072fc44963e253241df1fe33bc2c0decb1a69486dc82bb024686ced2.png" src="../../../_images/1db36cb7072fc44963e253241df1fe33bc2c0decb1a69486dc82bb024686ced2.png" />
 </div>
 </div>
 <p>Nodes are colored by the <code class="docutils literal notranslate"><span class="pre">cluster</span></code> property and labeled by <code class="docutils literal notranslate"><span class="pre">num_prop</span></code> property.
@@ -671,7 +671,7 @@ <h2>Example<a class="headerlink" href="#example" title="Permalink to this headin
 </div>
 </div>
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-<img alt="../../../_images/445d36e74e0b6388c5d537341184c54221ff96112f4e3820311e43490cdc046b.png" src="../../../_images/445d36e74e0b6388c5d537341184c54221ff96112f4e3820311e43490cdc046b.png" />
+<img alt="../../../_images/c5b25cadceb7d6c1e76fa5311c74e15290635f91390c8b4a5f6d55ac3f559444.png" src="../../../_images/c5b25cadceb7d6c1e76fa5311c74e15290635f91390c8b4a5f6d55ac3f559444.png" />
 </div>
 </div>
 <p>In the above plots only the nodes which are considered are colored and rest are

diff --git a/content/algorithms/dag/index.html b/content/algorithms/dag/index.html
@@ -500,7 +500,7 @@ <h3>Example<a class="headerlink" href="#example" title="Permalink to this headin
 </div>
 </div>
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-<img alt="../../../_images/71d2db9204dd41e1be57bf746a101c4f2a5694904b7d95ae1c0340ec167f7ad0.png" src="../../../_images/71d2db9204dd41e1be57bf746a101c4f2a5694904b7d95ae1c0340ec167f7ad0.png" />
+<img alt="../../../_images/9a3e38f488da906ed3f002d2cd46fa60b5f45fcf814a5186a809a5bd8d55984d.png" src="../../../_images/9a3e38f488da906ed3f002d2cd46fa60b5f45fcf814a5186a809a5bd8d55984d.png" />
 </div>
 </div>
 </section>
@@ -545,7 +545,7 @@ <h3>Example<a class="headerlink" href="#id1" title="Permalink to this heading">#
 </div>
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-<img alt="../../../_images/98e9735d58a5a7a5b36f636499d687d133e4804d163a60252cb659984d5d51da.png" src="../../../_images/98e9735d58a5a7a5b36f636499d687d133e4804d163a60252cb659984d5d51da.png" />
+<img alt="../../../_images/bd2798897e64006e46d352811def9a623ac563c549e6d00fc5f6785276323857.png" src="../../../_images/bd2798897e64006e46d352811def9a623ac563c549e6d00fc5f6785276323857.png" />
 </div>
 </div>
 <p>Here is a fun example of Professor Bumstead,
@@ -832,7 +832,8 @@ <h4>Combine all steps.<a class="headerlink" href="#combine-all-steps" title="Per
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>def topological_generations(G):
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>@nx._dispatch
+def topological_generations(G):
  &quot;&quot;&quot;Stratifies a DAG into generations.
 
  A topological generation is node collection in which ancestors of a node in each

diff --git a/content/algorithms/euler/euler.html b/content/algorithms/euler/euler.html
@@ -494,7 +494,7 @@ <h3>Reformulating the Problem in Abstract Terms<a class="headerlink" href="#refo
 </div>
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 <div class="cell_output docutils container">
-<img alt="../../../_images/de92a2760af666353fe74ce03451469b429dea35b9e67d3b48e16328e06b2f5b.png" src="../../../_images/de92a2760af666353fe74ce03451469b429dea35b9e67d3b48e16328e06b2f5b.png" />
+<img alt="../../../_images/de0e2385e62f5bc7840d2e730081656eaaa78bcaf2fca64d35ccbdae40c499e3.png" src="../../../_images/de0e2385e62f5bc7840d2e730081656eaaa78bcaf2fca64d35ccbdae40c499e3.png" />
 </div>
 </div>
 <p>Based on this abstraction, we can paraphrase the problem as follows:</p>
@@ -528,7 +528,7 @@ <h3>Euler’s Method<a class="headerlink" href="#euler-s-method" title="Permalin
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 <div class="cell_output docutils container">
-<img alt="../../../_images/4a493ba768cd1a3c312efccb5be84cd2d4e42c56730cbf2c171ce2e9a6068101.png" src="../../../_images/4a493ba768cd1a3c312efccb5be84cd2d4e42c56730cbf2c171ce2e9a6068101.png" />
+<img alt="../../../_images/fa8a39bc14f76ecba15f39ca6fe51e40a14e241bf8366b9ca1feb4e75e24c86c.png" src="../../../_images/fa8a39bc14f76ecba15f39ca6fe51e40a14e241bf8366b9ca1feb4e75e24c86c.png" />
 </div>
 </div>
 <p>He described his logic as follows:</p>
@@ -591,7 +591,7 @@ <h3>1. Eulerian Circuit Implementation<a class="headerlink" href="#eulerian-circ
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-<img alt="../../../_images/e665e7e236b30efbbdfafa01611139f4c0ddff32e30055d8d260ad2342ca6ad1.png" src="../../../_images/e665e7e236b30efbbdfafa01611139f4c0ddff32e30055d8d260ad2342ca6ad1.png" />
+<img alt="../../../_images/5eb190f4de018e35e0abc3a2f8df2bf801a4f1c41ce4a7c848d305fbe1c8fcd5.png" src="../../../_images/5eb190f4de018e35e0abc3a2f8df2bf801a4f1c41ce4a7c848d305fbe1c8fcd5.png" />
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@@ -741,7 +741,7 @@ <h3>3. Examples<a class="headerlink" href="#examples" title="Permalink to this h
 </div>
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-<img alt="../../../_images/a30f8f2c2c44d4e5830e120521a87a43bbfc483009825ac40eaa90d6be2da0f2.png" src="../../../_images/a30f8f2c2c44d4e5830e120521a87a43bbfc483009825ac40eaa90d6be2da0f2.png" />
+<img alt="../../../_images/74100bbd25b89542401e4303c3d6011ba7718e9df7d5cda81be84cc33d0b5f97.png" src="../../../_images/74100bbd25b89542401e4303c3d6011ba7718e9df7d5cda81be84cc33d0b5f97.png" />
 </div>
 </div>
 <p>The answer is No! All nodes except for the one in the center have exactly 3 edges in the wheel graph. Thus, it cannot have an Eulerian Path.</p>

diff --git a/content/algorithms/flow/dinitz_alg.html b/content/algorithms/flow/dinitz_alg.html
@@ -509,7 +509,7 @@ <h3>Motivation<a class="headerlink" href="#motivation" title="Permalink to this
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-<img alt="../../../_images/e8f3a3f418a11e44530849f0f395f718704d6f06242888ed26ab3ca9e5c54733.png" src="../../../_images/e8f3a3f418a11e44530849f0f395f718704d6f06242888ed26ab3ca9e5c54733.png" />
+<img alt="../../../_images/e7cabec7a0ed3d046ef4527abec72b080dfadc2d0ded4043aab4030f5473f56c.png" src="../../../_images/e7cabec7a0ed3d046ef4527abec72b080dfadc2d0ded4043aab4030f5473f56c.png" />
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 <p>So how shall you plan the paths of the data packets to send them in the least amount
@@ -538,7 +538,7 @@ <h3>Formalization<a class="headerlink" href="#formalization" title="Permalink to
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-<img alt="../../../_images/12258695685d14642ebe13e6dad5fd02008ab8afaffcb8b2639ce4ed02e48883.png" src="../../../_images/12258695685d14642ebe13e6dad5fd02008ab8afaffcb8b2639ce4ed02e48883.png" />
+<img alt="../../../_images/bff87c2250ad3e801463bb2bb79071717aaf7fd25ab56c3862d1f76b3a3ba9c7.png" src="../../../_images/bff87c2250ad3e801463bb2bb79071717aaf7fd25ab56c3862d1f76b3a3ba9c7.png" />
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 <p>Now say that node <span class="math notranslate nohighlight">\(u\)</span> and node <span class="math notranslate nohighlight">\(v\)</span> are connected and the maximum data per second that
@@ -557,7 +557,7 @@ <h3>Formalization<a class="headerlink" href="#formalization" title="Permalink to
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-<img alt="../../../_images/b40ce6e13570ed83a7af7308c6fff4639f34104f7c89f6cf0fbc15fbe8b7e7cb.png" src="../../../_images/b40ce6e13570ed83a7af7308c6fff4639f34104f7c89f6cf0fbc15fbe8b7e7cb.png" />
+<img alt="../../../_images/7e8525b2ceaeb41000c0be4a823fb94efc9e5a7a081d9d56a0aee807d1a09ea7.png" src="../../../_images/7e8525b2ceaeb41000c0be4a823fb94efc9e5a7a081d9d56a0aee807d1a09ea7.png" />
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 <p>So before go ahead and plan the paths on which we will be sending the data packets,
@@ -651,7 +651,7 @@ <h3>Formalization<a class="headerlink" href="#formalization" title="Permalink to
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-<img alt="../../../_images/2c0a0a3ac5410bc885af0c7718eb0ec3c6fc1598d7a76394f3d12bf221b3beb1.png" src="../../../_images/2c0a0a3ac5410bc885af0c7718eb0ec3c6fc1598d7a76394f3d12bf221b3beb1.png" />
+<img alt="../../../_images/685b60e82945a40ea761f254fe10f977483e67aacc3566c833bd091c8d8b68a8.png" src="../../../_images/685b60e82945a40ea761f254fe10f977483e67aacc3566c833bd091c8d8b68a8.png" />
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 <p>example of invalid flow:</p>
@@ -685,7 +685,7 @@ <h3>Formalization<a class="headerlink" href="#formalization" title="Permalink to
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-<img alt="../../../_images/d5ba68088f1a20e5791526e7d0a6ce705f40e2adb1c54f5efcb2b6060f4369b5.png" src="../../../_images/d5ba68088f1a20e5791526e7d0a6ce705f40e2adb1c54f5efcb2b6060f4369b5.png" />
+<img alt="../../../_images/324fe0db192c47e762395ec703622672ca44695220608dbc9c59d09acbb9114e.png" src="../../../_images/324fe0db192c47e762395ec703622672ca44695220608dbc9c59d09acbb9114e.png" />
 </div>
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 <p>red color edges dont satisfy capacity constraint and red color nodes dont satisfy the
@@ -786,7 +786,7 @@ <h3>Residual Capacity &amp; Graph<a class="headerlink" href="#residual-capacity-
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-<img alt="../../../_images/aa5523f255a9cbf5aa270ffc77c7432258c014c3f1345250cc00a6762957e742.png" src="../../../_images/aa5523f255a9cbf5aa270ffc77c7432258c014c3f1345250cc00a6762957e742.png" />
+<img alt="../../../_images/15cfa4b03c1ccfc6bd8ca3f711294e4b874e0e949d01855684ea3117c51cadcf.png" src="../../../_images/15cfa4b03c1ccfc6bd8ca3f711294e4b874e0e949d01855684ea3117c51cadcf.png" />
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 <p>This is the residual network for the flow shown above:</p>
@@ -798,7 +798,7 @@ <h3>Residual Capacity &amp; Graph<a class="headerlink" href="#residual-capacity-
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-<img alt="../../../_images/f9429e46be9cd8bf7b8d6c743ad55b56f18d61bd685e7974ccdfdcc085287671.png" src="../../../_images/f9429e46be9cd8bf7b8d6c743ad55b56f18d61bd685e7974ccdfdcc085287671.png" />
+<img alt="../../../_images/061acc09d55a1c5e56fe52bbf0505fc452cd027318d0c9c17155e7c1b1d98d2a.png" src="../../../_images/061acc09d55a1c5e56fe52bbf0505fc452cd027318d0c9c17155e7c1b1d98d2a.png" />
 </div>
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 <p>Note: In residual network we consider both the <span class="math notranslate nohighlight">\(uv\)</span> and <span class="math notranslate nohighlight">\(vu\)</span> edges if any of them is in <span class="math notranslate nohighlight">\(N\)</span></p>
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-<img alt="../../../_images/7d7a45289beb15b01ebc36282c08209b6d68d2a7f34338462f9f2defd68b3ec2.png" src="../../../_images/7d7a45289beb15b01ebc36282c08209b6d68d2a7f34338462f9f2defd68b3ec2.png" />
+<img alt="../../../_images/c95eca321dd69f5834930f5a9c455bd1abad6c8f0f4939559123af7ab87ec4ef.png" src="../../../_images/c95eca321dd69f5834930f5a9c455bd1abad6c8f0f4939559123af7ab87ec4ef.png" />
 </div>
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 <p>Note that if sink node <span class="math notranslate nohighlight">\(t\)</span> is not reachable from the source node <span class="math notranslate nohighlight">\(s\)</span> that means that no
@@ -937,7 +937,7 @@ <h3>Augmenting Path &amp; Flow<a class="headerlink" href="#augmenting-path-flow"
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-<img alt="../../../_images/fd7040636ae2ea856710eab2419fd5ae87a093f5ad245c14cf4c314345a87d47.png" src="../../../_images/fd7040636ae2ea856710eab2419fd5ae87a093f5ad245c14cf4c314345a87d47.png" />
+<img alt="../../../_images/8a1d27f0c0b8e9dd0da760c40afdd0aa0cf0d3380c80b71997a53e1c28c75851.png" src="../../../_images/8a1d27f0c0b8e9dd0da760c40afdd0aa0cf0d3380c80b71997a53e1c28c75851.png" />
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 <p>Augmenting path after augmenting:</p>
@@ -960,7 +960,7 @@ <h3>Augmenting Path &amp; Flow<a class="headerlink" href="#augmenting-path-flow"
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-<img alt="../../../_images/faa8aef1cba7a64a8fe98505a549452b471f5bf7c59afdae0cae35fdca01a11c.png" src="../../../_images/faa8aef1cba7a64a8fe98505a549452b471f5bf7c59afdae0cae35fdca01a11c.png" />
+<img alt="../../../_images/3eb55fc7945a078ab08dc60dc835373596fbe36d90245fe95537cdd0f2569a99.png" src="../../../_images/3eb55fc7945a078ab08dc60dc835373596fbe36d90245fe95537cdd0f2569a99.png" />
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 <p>Resulting new residual Network:</p>
@@ -975,7 +975,7 @@ <h3>Augmenting Path &amp; Flow<a class="headerlink" href="#augmenting-path-flow"
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-<img alt="../../../_images/804aafc70c6a1d494dbbd215a02f02897fb715374ef374a7842010c2a8aa05c6.png" src="../../../_images/804aafc70c6a1d494dbbd215a02f02897fb715374ef374a7842010c2a8aa05c6.png" />
+<img alt="../../../_images/32b86c8e8bb165bf131884d0764d820241b7fe8f3acb5b5644505b6178852a7c.png" src="../../../_images/32b86c8e8bb165bf131884d0764d820241b7fe8f3acb5b5644505b6178852a7c.png" />
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 <p>Each of the above steps plays a role in Dinitz’s algorithm for finding the
@@ -1044,7 +1044,7 @@ <h2>Maximum flow in NetworkX<a class="headerlink" href="#maximum-flow-in-network
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-<img alt="../../../_images/b57787abe826821eb7f75067b8c6fb319eba0535d27f1f1dd9a7b76d2c5d3f92.png" src="../../../_images/b57787abe826821eb7f75067b8c6fb319eba0535d27f1f1dd9a7b76d2c5d3f92.png" />
+<img alt="../../../_images/335df2f1069d9b6eae95e939daa18853a2980e1b22be60648e5ee9eb23918d73.png" src="../../../_images/335df2f1069d9b6eae95e939daa18853a2980e1b22be60648e5ee9eb23918d73.png" />
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 <p>Note: Iteration are stopped if the maximum flow found so far exceeds the cutoff value</p>
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-<img alt="../../../_images/44eb84181efad73acca55b690d870c7e6d5684f9d16a83e2c583d2df8df464ff.png" src="../../../_images/44eb84181efad73acca55b690d870c7e6d5684f9d16a83e2c583d2df8df464ff.png" />
+<img alt="../../../_images/313b617aa14b72b8751b9f7c13478983e66fdb99eef364d17bc9875fa6a6de74.png" src="../../../_images/313b617aa14b72b8751b9f7c13478983e66fdb99eef364d17bc9875fa6a6de74.png" />
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@@ -1153,7 +1153,7 @@ <h2>Reductions and Applications<a class="headerlink" href="#reductions-and-appli
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-<img alt="../../../_images/438f16173e9dd9ba313d2b1b71a28ef24fcf25fa4ee08ef84165eccc69d67fae.png" src="../../../_images/438f16173e9dd9ba313d2b1b71a28ef24fcf25fa4ee08ef84165eccc69d67fae.png" />
+<img alt="../../../_images/289a0738b07a35c010d7d15d7aa0183934119c5b0043eb2bdf9b552086195759.png" src="../../../_images/289a0738b07a35c010d7d15d7aa0183934119c5b0043eb2bdf9b552086195759.png" />
 </div>
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 <p>Above we can see a matching of intermediate shipping points and customers which

diff --git a/content/algorithms/isomorphism/isomorphism.html b/content/algorithms/isomorphism/isomorphism.html
@@ -477,7 +477,7 @@ <h2>What is isomorphism? Why is it interesting?<a class="headerlink" href="#what
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-<img alt="../../../_images/d2e0a7742e6f19b0ccb03ac777efbc2481f04b8d511c61406676e7da464b424c.png" src="../../../_images/d2e0a7742e6f19b0ccb03ac777efbc2481f04b8d511c61406676e7da464b424c.png" />
+<img alt="../../../_images/ca67a9662b6b1caace2c38c4f74adc818a80636613e6edca8e50d18dcbad8a1b.png" src="../../../_images/ca67a9662b6b1caace2c38c4f74adc818a80636613e6edca8e50d18dcbad8a1b.png" />
 </div>
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 <p>The spatial representations of these two graphs are very different yet
@@ -532,7 +532,7 @@ <h2>Isomorphism Algorithms<a class="headerlink" href="#isomorphism-algorithms" t
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-<img alt="../../../_images/a77c11d533f07bed55d938ec56bba029c3c90fb049a15166e34d9bc9056a2609.png" src="../../../_images/a77c11d533f07bed55d938ec56bba029c3c90fb049a15166e34d9bc9056a2609.png" />
+<img alt="../../../_images/11c58be7f4e96868e970fa58663cdb0f8e94cdca3675c4c79eaeda1cd34ce501.png" src="../../../_images/11c58be7f4e96868e970fa58663cdb0f8e94cdca3675c4c79eaeda1cd34ce501.png" />
 </div>
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 <p>We can use the function <code class="docutils literal notranslate"><span class="pre">nx.faster_could_be_isomorphic()</span></code> that returns True if G and H have the same degree secuence.</p>
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+<img alt="../../../_images/558b390cc7a863600e25baf0a60a655c8016056aab3a16ed60ee4b6f3f460a75.png" src="../../../_images/558b390cc7a863600e25baf0a60a655c8016056aab3a16ed60ee4b6f3f460a75.png" />
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diff --git a/content/algorithms/lca/LCA.html b/content/algorithms/lca/LCA.html
@@ -504,7 +504,7 @@ <h2>Example<a class="headerlink" href="#example" title="Permalink to this headin
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-<img alt="../../../_images/f1abf641d210e18ddf5caa8d567b6024272dd97ff1fa7a25fa9077c8a2262126.png" src="../../../_images/f1abf641d210e18ddf5caa8d567b6024272dd97ff1fa7a25fa9077c8a2262126.png" />
+<img alt="../../../_images/386c566201cdda503b97437ff0297f8942e023db95fad90971a217c614fd44de.png" src="../../../_images/386c566201cdda503b97437ff0297f8942e023db95fad90971a217c614fd44de.png" />
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 <p>Consider the tree above and observe the following relationships:</p>
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