add: hierarchical clustering

Author: BeaMarton13

doc/source/community_detection_guide/notebooks/community_detection_algorithms.ipynb

@@ -10,7 +10,7 @@
     "Modularity maximization methods are a prominent class of algorithms in community detection that aim to discover partitions of a network by optimizing a specific quality function called modularity.\n",
     "<div style=\"background-color: #e6ffe6; padding: 0px; border-radius: 5px;\">\n",
     "    \n",
-    "**NOTE:** You can find a more detailed explanation of **modularity** [here](./modularity.ipynb).\n",
+    "**NOTE:** You can find a more detailed explanation of **modularity** [here](./modularityZ.ipynb).\n",
     "\n",
     "</div>\n",
     "\n",
@@ -45,7 +45,7 @@
     "    - γ > 1: Leads to more, smaller, and well-connected communities.\n",
     "\n",
     "    - 0 < γ < 1: Leads to fewer, larger, and potentially less well-connected communities.\n",
-    "\n",
+    " \n",
     "\n",
     "### __community_fastgreedy__\n",
     "\n",
@@ -60,6 +60,34 @@
     "- _Hierarchical insights are valuable:_ As an agglomerative method, it constructs a dendrogram (a hierarchical tree of merges). In `igraph`, this function directly returns a `VertexDendrogram` object, which can be used to visualize community formation. From this dendrogram, the partition with the highest modularity found throughout the merging process can be easily extracted (e.g., using the `.as_clustering()` method), or other levels of granularity can be explored.\"\n",
     "\n",
     "- _Baseline comparison:_ Due to its historical significance and speed, it's often used as a baseline algorithm to compare the performance and results of newer, more complex community detection methods.\n",
+    " \n",
+    "\n",
+    "## __Hierarchical clustering__\n",
+    "Hierarchical clustering methods are a class of algorithms that build a hierarchy of partitions, either by merging smaller communities into larger ones or by subdividing a large network into smaller ones. The result of these methods is typically a **dendrogram**, which visually represents the nested community structure.\n",
+    "\n",
+    "These methods don't require you to pre-specify the number of communities. Instead, you choose the final partition by cutting the dendrogram at a particular level, which defines the number and size of the resulting communities.\n",
+    "<div style=\"background-color: #e6ffe6; padding: 0px; border-radius: 5px;\">\n",
+    "    \n",
+    "**NOTE:** You can find a more detailed explanation of **hierarchical clustering** [here](./hierarchical_clustering.ipynb).\n",
+    "\n",
+    "</div>\n",
+    "\n",
+    "\n",
+    "### __community_edge_betweenness (The Girvan-Newman Algorithm)__\n",
+    "\n",
+    "#### When is community_edge_betweenness applied?\n",
+    "\n",
+    "The Edge Betweenness (Girvan-Newman) algorithm is typically applied when:\n",
+    "\n",
+    "- _Identifying \"Bridge\" Edges is Key:_ The fundamental idea behind edge betweenness for community detection is that edges connecting different communities will have a high betweenness centrality because many shortest paths between nodes in separate communities must pass through them. Therefore, it's used when the goal is to pinpoint and remove these inter-community \"bottleneck\" connections to reveal the underlying groups.\n",
+    "\n",
+    "- _For a Divisive Approach to Community Detection:_ Unlike algorithms that build communities up (agglomerative), community_edge_betweenness employs a \"top-down\" or \"divisive\" strategy. It iteratively removes the most central \"bridge\" edges, causing the network to naturally break apart into its constituent communities. This is useful when you want to understand how communities are _separated_ rather than how they are _formed_.\n",
+    "\n",
+    "- _To Understand Hierarchical Community Structure:_ A significant strength of this method is that it intrinsically generates a hierarchical decomposition of the network. As edges are progressively removed, you can observe the community structure at different levels of granularity – from a few large communities to many smaller ones. This makes it ideal for analyses where understanding the nested relationships between groups is important, often visualized as a dendrogram.\n",
+    "\n",
+    "- _For Moderate-Sized Networks (or when computational resources allow for larger ones):_ A key consideration is the computational cost. Calculating and recalculating edge betweenness after each edge removal can be computationally intensive, especially for very large networks (it has a high time complexity, often cited as O(MN2) or O(N3) in dense graphs, where N is the number of nodes and M is the number of edges). Therefore, it's often more practical for small to medium-sized networks, or when approximate versions are available or high-performance computing resources can be leveraged.\n",
+    "\n",
+    "## __Other methods__\n",
     "\n",
     "\n",
     "### __community_voronoi__\n",
@@ -105,21 +133,6 @@
     "- _Computational efficiency for large graphs is a priority:_ The algorithm is generally quite efficient and scalable, making it a viable option for large networks where other methods might be too slow. It converges relatively quickly.\n",
     "\n",
     "\n",
-    "### __community_edge_betweenness (The Girvan-Newman Algorithm)__\n",
-    "\n",
-    "#### When is community_edge_betweenness applied?\n",
-    "\n",
-    "The Edge Betweenness (Girvan-Newman) algorithm is typically applied when:\n",
-    "\n",
-    "- _Identifying \"Bridge\" Edges is Key:_ The fundamental idea behind edge betweenness for community detection is that edges connecting different communities will have a high betweenness centrality because many shortest paths between nodes in separate communities must pass through them. Therefore, it's used when the goal is to pinpoint and remove these inter-community \"bottleneck\" connections to reveal the underlying groups.\n",
-    "\n",
-    "- _For a Divisive Approach to Community Detection:_ Unlike algorithms that build communities up (agglomerative), community_edge_betweenness employs a \"top-down\" or \"divisive\" strategy. It iteratively removes the most central \"bridge\" edges, causing the network to naturally break apart into its constituent communities. This is useful when you want to understand how communities are _separated_ rather than how they are _formed_.\n",
-    "\n",
-    "- _To Understand Hierarchical Community Structure:_ A significant strength of this method is that it intrinsically generates a hierarchical decomposition of the network. As edges are progressively removed, you can observe the community structure at different levels of granularity – from a few large communities to many smaller ones. This makes it ideal for analyses where understanding the nested relationships between groups is important, often visualized as a dendrogram.\n",
-    "\n",
-    "- _For Moderate-Sized Networks (or when computational resources allow for larger ones):_ A key consideration is the computational cost. Calculating and recalculating edge betweenness after each edge removal can be computationally intensive, especially for very large networks (it has a high time complexity, often cited as O(MN2) or O(N3) in dense graphs, where N is the number of nodes and M is the number of edges). Therefore, it's often more practical for small to medium-sized networks, or when approximate versions are available or high-performance computing resources can be leveraged.\n",
-    "\n",
-    "\n",
     "### __community_label_propagation__\n",
     "\n",
     "#### When is community_label_propagation applied?\n",