Update app.py

app.py

@@ -37,52 +37,29 @@ if sidebar_option == "Introductory Tutorial":
         ("Basic: Simple Graph Directed", "Directed graphs have edges with a direction. They are useful for workflows or dependencies. For example, in a project plan, a directed graph might show tasks with arrows indicating the order in which they need to be completed."),
         ("Drawing: Custom Node Position", "This feature allows you to manually set where each node appears on the graph. For example, in a family tree, you might want to position nodes to reflect generational hierarchies rather than relying on an automatic layout."),
         ("Drawing: Cluster Layout", "Nodes are grouped into clusters based on their connections. For instance, in a network of social media users, this could highlight friend groups. Each group would appear as a tight cluster in the visualization."),
-        ("Drawing: Degree Analysis", "This visualizes the connections (or degree) of nodes. For example, in a transportation network, hubs like airports can be highlighted because they have the highest degree, representing more connections to other nodes.
-"),
-        ("Drawing: Ego Graph", "Focuses on a single node and its immediate connections. For instance, if you want to see all direct friends of a specific person on a social network, this feature isolates that person and their relationships.
-"),
-        ("Drawing: Eigenvalues", "Eigenvalues come from the graph’s Laplacian matrix and reveal structural properties. For example, in community detection, eigenvalues can help identify clusters or measure the connectivity of a graph.
-"),
-        ("Drawing: House With Colors", "Displays a basic "house graph," a simple structure that resembles a house. For example, you could use it for teaching graph theory basics, with color-coded nodes and edges representing different parts of the structure.
-"),
-        ("Drawing: Labels and Colors", "This lets you customize the appearance of nodes and edges by adding labels or colors. For example, in a roadmap, cities (nodes) can be color-coded by region, and roads (edges) can have labels for distance.
-"),
-        ("Drawing: Multipartite Layout", "Creates multipartite graphs where nodes are divided into layers, and edges only connect nodes from different layers. For instance, in a university, one layer could represent professors and another students, with edges indicating which professor teaches which student.
-"),
-        ("Drawing: Node Colormap", "Applies color gradients to nodes based on their properties, like degree or centrality. For example, nodes in a social network can be shaded to show influence, with darker colors for highly connected individuals.
-"),
-        ("Drawing: Rainbow Coloring", "This colorful feature assigns different colors to edges, helping differentiate them. For example, in a circular graph, this can show the relative positions of connections, making it visually appealing.
-"),
-        ("Drawing: Random Geometric Graph", "Generates graphs where nodes are connected if they’re within a specific distance. For example, in a wireless sensor network, nodes represent sensors, and edges show connectivity based on signal range.
-"),
-        ("Drawing: Self-loops", "Visualizes edges that start and end at the same node. For example, in a citation network, a self-loop could represent a researcher citing their previous work.
-"),
-        ("Drawing: Simple Path", "Displays simple linear graphs where nodes connect in a sequence. For example, it could represent a production line where each step depends on the previous one.
-"),
-        ("Drawing: Spectral Embedding", "Uses a mathematical technique to arrange nodes in a lower-dimensional space. For example, you can visualize clusters in a high-dimensional dataset in a way that preserves their relationships.
-"),
-        ("Drawing: Traveling Salesman Problem", "Visualizes solutions to the Traveling Salesman Problem (TSP), where the goal is to find the shortest route visiting every node once. For example, a delivery route optimization can use this to minimize travel costs.
-"),
-        ("Drawing: Weighted Graph", "Shows graphs with weighted edges. For example, in a flight network, edge weights can represent ticket prices or distances, with thicker edges for higher weights.
-"),
-        ("3D Drawing: Animations of 3D Rotation", "Generates 3D graphs with rotation animations. For example, you can visualize molecule structures or spatial relationships dynamically.
-"),
-        ("3D Drawing: Basic Matplotlib", "Creates 3D graph visualizations using Matplotlib, letting you explore spatial relationships. For example, you could map a city’s buildings in 3D space.
-"),
-        ("Graph: DAG - Topological Layout", "Displays Directed Acyclic Graphs (DAGs) in a topological order. For example, it can represent workflows or dependency graphs where tasks need to follow a sequence.
-"),
-        ("Graph: Erdos Renyi", "Generates random graphs where edges appear based on a probability. For example, you can model random connections in a network to study statistical properties.
-"),
-        ("Graph: Karate Club", "This graph is a classic benchmark in network science, showing relationships in a club. It’s often used for community detection and teaching graph analysis.
-"),
-        ("Graph: Minimum Spanning Tree", "Extracts a tree from the graph connecting all nodes with the minimum total edge weight. For example, this is used in network design to minimize cable or pipeline costs.
-"),
-        ("Graph: Triads", "Analyzes three-node structures (triads). For example, in social networks, closed triads (triangles) indicate strong relationships among three people.
-"),
-        ("Algorithms: Cycle Detection", "Detects cycles in graphs, useful for spotting feedback loops or circular dependencies. For example, in a dependency graph, it can help identify tasks that reference each other.
-"),
-        ("Algorithms: Greedy Coloring", "Colors nodes so that no two adjacent nodes share the same color. For example, in exam scheduling, this ensures no two overlapping exams are assigned the same room.
-")
+        ("Drawing: Degree Analysis", "This visualizes the connections (or degree) of nodes. For example, in a transportation network, hubs like airports can be highlighted because they have the highest degree, representing more connections to other nodes."),
+        ("Drawing: Ego Graph", "Focuses on a single node and its immediate connections. For instance, if you want to see all direct friends of a specific person on a social network, this feature isolates that person and their relationships."),
+        ("Drawing: Eigenvalues", "Eigenvalues come from the graph’s Laplacian matrix and reveal structural properties. For example, in community detection, eigenvalues can help identify clusters or measure the connectivity of a graph."),
+        ("Drawing: House With Colors", "Displays a basic "house graph," a simple structure that resembles a house. For example, you could use it for teaching graph theory basics, with color-coded nodes and edges representing different parts of the structure."),
+        ("Drawing: Labels and Colors", "This lets you customize the appearance of nodes and edges by adding labels or colors. For example, in a roadmap, cities (nodes) can be color-coded by region, and roads (edges) can have labels for distance."),
+        ("Drawing: Multipartite Layout", "Creates multipartite graphs where nodes are divided into layers, and edges only connect nodes from different layers. For instance, in a university, one layer could represent professors and another students, with edges indicating which professor teaches which student."),
+        ("Drawing: Node Colormap", "Applies color gradients to nodes based on their properties, like degree or centrality. For example, nodes in a social network can be shaded to show influence, with darker colors for highly connected individuals."),
+        ("Drawing: Rainbow Coloring", "This colorful feature assigns different colors to edges, helping differentiate them. For example, in a circular graph, this can show the relative positions of connections, making it visually appealing."),
+        ("Drawing: Random Geometric Graph", "Generates graphs where nodes are connected if they’re within a specific distance. For example, in a wireless sensor network, nodes represent sensors, and edges show connectivity based on signal range."),
+        ("Drawing: Self-loops", "Visualizes edges that start and end at the same node. For example, in a citation network, a self-loop could represent a researcher citing their previous work."),
+        ("Drawing: Simple Path", "Displays simple linear graphs where nodes connect in a sequence. For example, it could represent a production line where each step depends on the previous one."),
+        ("Drawing: Spectral Embedding", "Uses a mathematical technique to arrange nodes in a lower-dimensional space. For example, you can visualize clusters in a high-dimensional dataset in a way that preserves their relationships."),
+        ("Drawing: Traveling Salesman Problem", "Visualizes solutions to the Traveling Salesman Problem (TSP), where the goal is to find the shortest route visiting every node once. For example, a delivery route optimization can use this to minimize travel costs."),
+        ("Drawing: Weighted Graph", "Shows graphs with weighted edges. For example, in a flight network, edge weights can represent ticket prices or distances, with thicker edges for higher weights."),
+        ("3D Drawing: Animations of 3D Rotation", "Generates 3D graphs with rotation animations. For example, you can visualize molecule structures or spatial relationships dynamically."),
+        ("3D Drawing: Basic Matplotlib", "Creates 3D graph visualizations using Matplotlib, letting you explore spatial relationships. For example, you could map a city’s buildings in 3D space."),
+        ("Graph: DAG - Topological Layout", "Displays Directed Acyclic Graphs (DAGs) in a topological order. For example, it can represent workflows or dependency graphs where tasks need to follow a sequence."),
+        ("Graph: Erdos Renyi", "Generates random graphs where edges appear based on a probability. For example, you can model random connections in a network to study statistical properties."),
+        ("Graph: Karate Club", "This graph is a classic benchmark in network science, showing relationships in a club. It’s often used for community detection and teaching graph analysis."),
+        ("Graph: Minimum Spanning Tree", "Extracts a tree from the graph connecting all nodes with the minimum total edge weight. For example, this is used in network design to minimize cable or pipeline costs."),
+        ("Graph: Triads", "Analyzes three-node structures (triads). For example, in social networks, closed triads (triangles) indicate strong relationships among three people."),
+        ("Algorithms: Cycle Detection", "Detects cycles in graphs, useful for spotting feedback loops or circular dependencies. For example, in a dependency graph, it can help identify tasks that reference each other."),
+        ("Algorithms: Greedy Coloring", "Colors nodes so that no two adjacent nodes share the same color. For example, in exam scheduling, this ensures no two overlapping exams are assigned the same room.")
     ]
     
     for title, desc in descriptions: