Initial commit

skills/networkx/SKILL.md

@@ -0,0 +1,431 @@
+---
+name: networkx
+description: Comprehensive toolkit for creating, analyzing, and visualizing complex networks and graphs in Python. Use when working with network/graph data structures, analyzing relationships between entities, computing graph algorithms (shortest paths, centrality, clustering), detecting communities, generating synthetic networks, or visualizing network topologies. Applicable to social networks, biological networks, transportation systems, citation networks, and any domain involving pairwise relationships.
+---
+
+# NetworkX
+
+## Overview
+
+NetworkX is a Python package for creating, manipulating, and analyzing complex networks and graphs. Use this skill when working with network or graph data structures, including social networks, biological networks, transportation systems, citation networks, knowledge graphs, or any system involving relationships between entities.
+
+## When to Use This Skill
+
+Invoke this skill when tasks involve:
+
+- **Creating graphs**: Building network structures from data, adding nodes and edges with attributes
+- **Graph analysis**: Computing centrality measures, finding shortest paths, detecting communities, measuring clustering
+- **Graph algorithms**: Running standard algorithms like Dijkstra's, PageRank, minimum spanning trees, maximum flow
+- **Network generation**: Creating synthetic networks (random, scale-free, small-world models) for testing or simulation
+- **Graph I/O**: Reading from or writing to various formats (edge lists, GraphML, JSON, CSV, adjacency matrices)
+- **Visualization**: Drawing and customizing network visualizations with matplotlib or interactive libraries
+- **Network comparison**: Checking isomorphism, computing graph metrics, analyzing structural properties
+
+## Core Capabilities
+
+### 1. Graph Creation and Manipulation
+
+NetworkX supports four main graph types:
+- **Graph**: Undirected graphs with single edges
+- **DiGraph**: Directed graphs with one-way connections
+- **MultiGraph**: Undirected graphs allowing multiple edges between nodes
+- **MultiDiGraph**: Directed graphs with multiple edges
+
+Create graphs by:
+```python
+import networkx as nx
+
+# Create empty graph
+G = nx.Graph()
+
+# Add nodes (can be any hashable type)
+G.add_node(1)
+G.add_nodes_from([2, 3, 4])
+G.add_node("protein_A", type='enzyme', weight=1.5)
+
+# Add edges
+G.add_edge(1, 2)
+G.add_edges_from([(1, 3), (2, 4)])
+G.add_edge(1, 4, weight=0.8, relation='interacts')
+```
+
+**Reference**: See `references/graph-basics.md` for comprehensive guidance on creating, modifying, examining, and managing graph structures, including working with attributes and subgraphs.
+
+### 2. Graph Algorithms
+
+NetworkX provides extensive algorithms for network analysis:
+
+**Shortest Paths**:
+```python
+# Find shortest path
+path = nx.shortest_path(G, source=1, target=5)
+length = nx.shortest_path_length(G, source=1, target=5, weight='weight')
+```
+
+**Centrality Measures**:
+```python
+# Degree centrality
+degree_cent = nx.degree_centrality(G)
+
+# Betweenness centrality
+betweenness = nx.betweenness_centrality(G)
+
+# PageRank
+pagerank = nx.pagerank(G)
+```
+
+**Community Detection**:
+```python
+from networkx.algorithms import community
+
+# Detect communities
+communities = community.greedy_modularity_communities(G)
+```
+
+**Connectivity**:
+```python
+# Check connectivity
+is_connected = nx.is_connected(G)
+
+# Find connected components
+components = list(nx.connected_components(G))
+```
+
+**Reference**: See `references/algorithms.md` for detailed documentation on all available algorithms including shortest paths, centrality measures, clustering, community detection, flows, matching, tree algorithms, and graph traversal.
+
+### 3. Graph Generators
+
+Create synthetic networks for testing, simulation, or modeling:
+
+**Classic Graphs**:
+```python
+# Complete graph
+G = nx.complete_graph(n=10)
+
+# Cycle graph
+G = nx.cycle_graph(n=20)
+
+# Known graphs
+G = nx.karate_club_graph()
+G = nx.petersen_graph()
+```
+
+**Random Networks**:
+```python
+# Erdős-Rényi random graph
+G = nx.erdos_renyi_graph(n=100, p=0.1, seed=42)
+
+# Barabási-Albert scale-free network
+G = nx.barabasi_albert_graph(n=100, m=3, seed=42)
+
+# Watts-Strogatz small-world network
+G = nx.watts_strogatz_graph(n=100, k=6, p=0.1, seed=42)
+```
+
+**Structured Networks**:
+```python
+# Grid graph
+G = nx.grid_2d_graph(m=5, n=7)
+
+# Random tree
+G = nx.random_tree(n=100, seed=42)
+```
+
+**Reference**: See `references/generators.md` for comprehensive coverage of all graph generators including classic, random, lattice, bipartite, and specialized network models with detailed parameters and use cases.
+
+### 4. Reading and Writing Graphs
+
+NetworkX supports numerous file formats and data sources:
+
+**File Formats**:
+```python
+# Edge list
+G = nx.read_edgelist('graph.edgelist')
+nx.write_edgelist(G, 'graph.edgelist')
+
+# GraphML (preserves attributes)
+G = nx.read_graphml('graph.graphml')
+nx.write_graphml(G, 'graph.graphml')
+
+# GML
+G = nx.read_gml('graph.gml')
+nx.write_gml(G, 'graph.gml')
+
+# JSON
+data = nx.node_link_data(G)
+G = nx.node_link_graph(data)
+```
+
+**Pandas Integration**:
+```python
+import pandas as pd
+
+# From DataFrame
+df = pd.DataFrame({'source': [1, 2, 3], 'target': [2, 3, 4], 'weight': [0.5, 1.0, 0.75]})
+G = nx.from_pandas_edgelist(df, 'source', 'target', edge_attr='weight')
+
+# To DataFrame
+df = nx.to_pandas_edgelist(G)
+```
+
+**Matrix Formats**:
+```python
+import numpy as np
+
+# Adjacency matrix
+A = nx.to_numpy_array(G)
+G = nx.from_numpy_array(A)
+
+# Sparse matrix
+A = nx.to_scipy_sparse_array(G)
+G = nx.from_scipy_sparse_array(A)
+```
+
+**Reference**: See `references/io.md` for complete documentation on all I/O formats including CSV, SQL databases, Cytoscape, DOT, and guidance on format selection for different use cases.
+
+### 5. Visualization
+
+Create clear and informative network visualizations:
+
+**Basic Visualization**:
+```python
+import matplotlib.pyplot as plt
+
+# Simple draw
+nx.draw(G, with_labels=True)
+plt.show()
+
+# With layout
+pos = nx.spring_layout(G, seed=42)
+nx.draw(G, pos=pos, with_labels=True, node_color='lightblue', node_size=500)
+plt.show()
+```
+
+**Customization**:
+```python
+# Color by degree
+node_colors = [G.degree(n) for n in G.nodes()]
+nx.draw(G, node_color=node_colors, cmap=plt.cm.viridis)
+
+# Size by centrality
+centrality = nx.betweenness_centrality(G)
+node_sizes = [3000 * centrality[n] for n in G.nodes()]
+nx.draw(G, node_size=node_sizes)
+
+# Edge weights
+edge_widths = [3 * G[u][v].get('weight', 1) for u, v in G.edges()]
+nx.draw(G, width=edge_widths)
+```
+
+**Layout Algorithms**:
+```python
+# Spring layout (force-directed)
+pos = nx.spring_layout(G, seed=42)
+
+# Circular layout
+pos = nx.circular_layout(G)
+
+# Kamada-Kawai layout
+pos = nx.kamada_kawai_layout(G)
+
+# Spectral layout
+pos = nx.spectral_layout(G)
+```
+
+**Publication Quality**:
+```python
+plt.figure(figsize=(12, 8))
+pos = nx.spring_layout(G, seed=42)
+nx.draw(G, pos=pos, node_color='lightblue', node_size=500,
+        edge_color='gray', with_labels=True, font_size=10)
+plt.title('Network Visualization', fontsize=16)
+plt.axis('off')
+plt.tight_layout()
+plt.savefig('network.png', dpi=300, bbox_inches='tight')
+plt.savefig('network.pdf', bbox_inches='tight')  # Vector format
+```
+
+**Reference**: See `references/visualization.md` for extensive documentation on visualization techniques including layout algorithms, customization options, interactive visualizations with Plotly and PyVis, 3D networks, and publication-quality figure creation.
+
+## Working with NetworkX
+
+### Installation
+
+Ensure NetworkX is installed:
+```python
+# Check if installed
+import networkx as nx
+print(nx.__version__)
+
+# Install if needed (via bash)
+# uv pip install networkx
+# uv pip install networkx[default]  # With optional dependencies
+```
+
+### Common Workflow Pattern
+
+Most NetworkX tasks follow this pattern:
+
+1. **Create or Load Graph**:
+   ```python
+   # From scratch
+   G = nx.Graph()
+   G.add_edges_from([(1, 2), (2, 3), (3, 4)])
+
+   # Or load from file/data
+   G = nx.read_edgelist('data.txt')
+   ```
+
+2. **Examine Structure**:
+   ```python
+   print(f"Nodes: {G.number_of_nodes()}")
+   print(f"Edges: {G.number_of_edges()}")
+   print(f"Density: {nx.density(G)}")
+   print(f"Connected: {nx.is_connected(G)}")
+   ```
+
+3. **Analyze**:
+   ```python
+   # Compute metrics
+   degree_cent = nx.degree_centrality(G)
+   avg_clustering = nx.average_clustering(G)
+
+   # Find paths
+   path = nx.shortest_path(G, source=1, target=4)
+
+   # Detect communities
+   communities = community.greedy_modularity_communities(G)
+   ```
+
+4. **Visualize**:
+   ```python
+   pos = nx.spring_layout(G, seed=42)
+   nx.draw(G, pos=pos, with_labels=True)
+   plt.show()
+   ```
+
+5. **Export Results**:
+   ```python
+   # Save graph
+   nx.write_graphml(G, 'analyzed_network.graphml')
+
+   # Save metrics
+   df = pd.DataFrame({
+       'node': list(degree_cent.keys()),
+       'centrality': list(degree_cent.values())
+   })
+   df.to_csv('centrality_results.csv', index=False)
+   ```
+
+### Important Considerations
+
+**Floating Point Precision**: When graphs contain floating-point numbers, all results are inherently approximate due to precision limitations. This can affect algorithm outcomes, particularly in minimum/maximum computations.
+
+**Memory and Performance**: Each time a script runs, graph data must be loaded into memory. For large networks:
+- Use appropriate data structures (sparse matrices for large sparse graphs)
+- Consider loading only necessary subgraphs
+- Use efficient file formats (pickle for Python objects, compressed formats)
+- Leverage approximate algorithms for very large networks (e.g., `k` parameter in centrality calculations)
+
+**Node and Edge Types**:
+- Nodes can be any hashable Python object (numbers, strings, tuples, custom objects)
+- Use meaningful identifiers for clarity
+- When removing nodes, all incident edges are automatically removed
+
+**Random Seeds**: Always set random seeds for reproducibility in random graph generation and force-directed layouts:
+```python
+G = nx.erdos_renyi_graph(n=100, p=0.1, seed=42)
+pos = nx.spring_layout(G, seed=42)
+```
+
+## Quick Reference
+
+### Basic Operations
+```python
+# Create
+G = nx.Graph()
+G.add_edge(1, 2)
+
+# Query
+G.number_of_nodes()
+G.number_of_edges()
+G.degree(1)
+list(G.neighbors(1))
+
+# Check
+G.has_node(1)
+G.has_edge(1, 2)
+nx.is_connected(G)
+
+# Modify
+G.remove_node(1)
+G.remove_edge(1, 2)
+G.clear()
+```
+
+### Essential Algorithms
+```python
+# Paths
+nx.shortest_path(G, source, target)
+nx.all_pairs_shortest_path(G)
+
+# Centrality
+nx.degree_centrality(G)
+nx.betweenness_centrality(G)
+nx.closeness_centrality(G)
+nx.pagerank(G)
+
+# Clustering
+nx.clustering(G)
+nx.average_clustering(G)
+
+# Components
+nx.connected_components(G)
+nx.strongly_connected_components(G)  # Directed
+
+# Community
+community.greedy_modularity_communities(G)
+```
+
+### File I/O Quick Reference
+```python
+# Read
+nx.read_edgelist('file.txt')
+nx.read_graphml('file.graphml')
+nx.read_gml('file.gml')
+
+# Write
+nx.write_edgelist(G, 'file.txt')
+nx.write_graphml(G, 'file.graphml')
+nx.write_gml(G, 'file.gml')
+
+# Pandas
+nx.from_pandas_edgelist(df, 'source', 'target')
+nx.to_pandas_edgelist(G)
+```
+
+## Resources
+
+This skill includes comprehensive reference documentation:
+
+### references/graph-basics.md
+Detailed guide on graph types, creating and modifying graphs, adding nodes and edges, managing attributes, examining structure, and working with subgraphs.
+
+### references/algorithms.md
+Complete coverage of NetworkX algorithms including shortest paths, centrality measures, connectivity, clustering, community detection, flow algorithms, tree algorithms, matching, coloring, isomorphism, and graph traversal.
+
+### references/generators.md
+Comprehensive documentation on graph generators including classic graphs, random models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz), lattices, trees, social network models, and specialized generators.
+
+### references/io.md
+Complete guide to reading and writing graphs in various formats: edge lists, adjacency lists, GraphML, GML, JSON, CSV, Pandas DataFrames, NumPy arrays, SciPy sparse matrices, database integration, and format selection guidelines.
+
+### references/visualization.md
+Extensive documentation on visualization techniques including layout algorithms, customizing node and edge appearance, labels, interactive visualizations with Plotly and PyVis, 3D networks, bipartite layouts, and creating publication-quality figures.
+
+## Additional Resources
+
+- **Official Documentation**: https://networkx.org/documentation/latest/
+- **Tutorial**: https://networkx.org/documentation/latest/tutorial.html
+- **Gallery**: https://networkx.org/documentation/latest/auto_examples/index.html
+- **GitHub**: https://github.com/networkx/networkx

skills/networkx/references/algorithms.md

@@ -0,0 +1,383 @@
+# NetworkX Graph Algorithms
+
+## Shortest Paths
+
+### Single Source Shortest Paths
+```python
+# Dijkstra's algorithm (weighted graphs)
+path = nx.shortest_path(G, source=1, target=5, weight='weight')
+length = nx.shortest_path_length(G, source=1, target=5, weight='weight')
+
+# All shortest paths from source
+paths = nx.single_source_shortest_path(G, source=1)
+lengths = nx.single_source_shortest_path_length(G, source=1)
+
+# Bellman-Ford (handles negative weights)
+path = nx.bellman_ford_path(G, source=1, target=5, weight='weight')
+```
+
+### All Pairs Shortest Paths
+```python
+# All pairs (returns iterator)
+for source, paths in nx.all_pairs_shortest_path(G):
+    print(f"From {source}: {paths}")
+
+# Floyd-Warshall algorithm
+lengths = dict(nx.all_pairs_shortest_path_length(G))
+```
+
+### Specialized Shortest Path Algorithms
+```python
+# A* algorithm (with heuristic)
+def heuristic(u, v):
+    # Custom heuristic function
+    return abs(u - v)
+
+path = nx.astar_path(G, source=1, target=5, heuristic=heuristic, weight='weight')
+
+# Average shortest path length
+avg_length = nx.average_shortest_path_length(G)
+```
+
+## Connectivity
+
+### Connected Components (Undirected)
+```python
+# Check if connected
+is_connected = nx.is_connected(G)
+
+# Number of components
+num_components = nx.number_connected_components(G)
+
+# Get all components (returns iterator of sets)
+components = list(nx.connected_components(G))
+largest_component = max(components, key=len)
+
+# Get component containing specific node
+component = nx.node_connected_component(G, node=1)
+```
+
+### Strong/Weak Connectivity (Directed)
+```python
+# Strong connectivity (mutually reachable)
+is_strongly_connected = nx.is_strongly_connected(G)
+strong_components = list(nx.strongly_connected_components(G))
+largest_scc = max(strong_components, key=len)
+
+# Weak connectivity (ignoring direction)
+is_weakly_connected = nx.is_weakly_connected(G)
+weak_components = list(nx.weakly_connected_components(G))
+
+# Condensation (DAG of strongly connected components)
+condensed = nx.condensation(G)
+```
+
+### Cuts and Connectivity
+```python
+# Minimum node/edge cut
+min_node_cut = nx.minimum_node_cut(G, s=1, t=5)
+min_edge_cut = nx.minimum_edge_cut(G, s=1, t=5)
+
+# Node/edge connectivity
+node_connectivity = nx.node_connectivity(G)
+edge_connectivity = nx.edge_connectivity(G)
+```
+
+## Centrality Measures
+
+### Degree Centrality
+```python
+# Fraction of nodes each node is connected to
+degree_cent = nx.degree_centrality(G)
+
+# For directed graphs
+in_degree_cent = nx.in_degree_centrality(G)
+out_degree_cent = nx.out_degree_centrality(G)
+```
+
+### Betweenness Centrality
+```python
+# Fraction of shortest paths passing through node
+betweenness = nx.betweenness_centrality(G, weight='weight')
+
+# Edge betweenness
+edge_betweenness = nx.edge_betweenness_centrality(G, weight='weight')
+
+# Approximate for large graphs
+approx_betweenness = nx.betweenness_centrality(G, k=100)  # Sample 100 nodes
+```
+
+### Closeness Centrality
+```python
+# Reciprocal of average shortest path length
+closeness = nx.closeness_centrality(G)
+
+# For disconnected graphs
+closeness = nx.closeness_centrality(G, wf_improved=True)
+```
+
+### Eigenvector Centrality
+```python
+# Centrality based on connections to high-centrality nodes
+eigenvector = nx.eigenvector_centrality(G, max_iter=1000)
+
+# Katz centrality (variant with attenuation factor)
+katz = nx.katz_centrality(G, alpha=0.1, beta=1.0)
+```
+
+### PageRank
+```python
+# Google's PageRank algorithm
+pagerank = nx.pagerank(G, alpha=0.85)
+
+# Personalized PageRank
+personalization = {node: 1.0 if node in [1, 2] else 0.0 for node in G}
+ppr = nx.pagerank(G, personalization=personalization)
+```
+
+## Clustering
+
+### Clustering Coefficients
+```python
+# Clustering coefficient for each node
+clustering = nx.clustering(G)
+
+# Average clustering coefficient
+avg_clustering = nx.average_clustering(G)
+
+# Weighted clustering
+weighted_clustering = nx.clustering(G, weight='weight')
+```
+
+### Transitivity
+```python
+# Overall clustering (ratio of triangles to triads)
+transitivity = nx.transitivity(G)
+```
+
+### Triangles
+```python
+# Count triangles per node
+triangles = nx.triangles(G)
+
+# Total number of triangles
+total_triangles = sum(triangles.values()) // 3
+```
+
+## Community Detection
+
+### Modularity-Based
+```python
+from networkx.algorithms import community
+
+# Greedy modularity maximization
+communities = community.greedy_modularity_communities(G)
+
+# Compute modularity
+modularity = community.modularity(G, communities)
+```
+
+### Label Propagation
+```python
+# Fast community detection
+communities = community.label_propagation_communities(G)
+```
+
+### Girvan-Newman
+```python
+# Hierarchical community detection via edge betweenness
+comp = community.girvan_newman(G)
+limited = itertools.takewhile(lambda c: len(c) <= 10, comp)
+for communities in limited:
+    print(tuple(sorted(c) for c in communities))
+```
+
+## Matching and Covering
+
+### Maximum Matching
+```python
+# Maximum cardinality matching
+matching = nx.max_weight_matching(G)
+
+# Check if matching is valid
+is_matching = nx.is_matching(G, matching)
+is_perfect = nx.is_perfect_matching(G, matching)
+```
+
+### Minimum Vertex/Edge Cover
+```python
+# Minimum set of nodes covering all edges
+min_vertex_cover = nx.approximation.min_weighted_vertex_cover(G)
+
+# Minimum edge dominating set
+min_edge_dom = nx.approximation.min_edge_dominating_set(G)
+```
+
+## Tree Algorithms
+
+### Minimum Spanning Tree
+```python
+# Kruskal's or Prim's algorithm
+mst = nx.minimum_spanning_tree(G, weight='weight')
+
+# Maximum spanning tree
+mst_max = nx.maximum_spanning_tree(G, weight='weight')
+
+# Enumerate all spanning trees
+all_spanning = nx.all_spanning_trees(G)
+```
+
+### Tree Properties
+```python
+# Check if graph is tree
+is_tree = nx.is_tree(G)
+is_forest = nx.is_forest(G)
+
+# For directed graphs
+is_arborescence = nx.is_arborescence(G)
+```
+
+## Flow and Capacity
+
+### Maximum Flow
+```python
+# Maximum flow value
+flow_value = nx.maximum_flow_value(G, s=1, t=5, capacity='capacity')
+
+# Maximum flow with flow dict
+flow_value, flow_dict = nx.maximum_flow(G, s=1, t=5, capacity='capacity')
+
+# Minimum cut
+cut_value, partition = nx.minimum_cut(G, s=1, t=5, capacity='capacity')
+```
+
+### Cost Flow
+```python
+# Minimum cost flow
+flow_dict = nx.min_cost_flow(G, demand='demand', capacity='capacity', weight='weight')
+cost = nx.cost_of_flow(G, flow_dict, weight='weight')
+```
+
+## Cycles
+
+### Finding Cycles
+```python
+# Simple cycles (for directed graphs)
+cycles = list(nx.simple_cycles(G))
+
+# Cycle basis (for undirected graphs)
+basis = nx.cycle_basis(G)
+
+# Check if acyclic
+is_dag = nx.is_directed_acyclic_graph(G)
+```
+
+### Topological Sorting
+```python
+# Only for DAGs
+try:
+    topo_order = list(nx.topological_sort(G))
+except nx.NetworkXError:
+    print("Graph has cycles")
+
+# All topological sorts
+all_topo = nx.all_topological_sorts(G)
+```
+
+## Cliques
+
+### Finding Cliques
+```python
+# All maximal cliques
+cliques = list(nx.find_cliques(G))
+
+# Maximum clique (NP-complete, approximate)
+max_clique = nx.approximation.max_clique(G)
+
+# Clique number
+clique_number = nx.graph_clique_number(G)
+
+# Number of maximal cliques containing each node
+clique_counts = nx.node_clique_number(G)
+```
+
+## Graph Coloring
+
+### Node Coloring
+```python
+# Greedy coloring
+coloring = nx.greedy_color(G, strategy='largest_first')
+
+# Different strategies: 'largest_first', 'smallest_last', 'random_sequential'
+coloring = nx.greedy_color(G, strategy='smallest_last')
+```
+
+## Isomorphism
+
+### Graph Isomorphism
+```python
+# Check if graphs are isomorphic
+is_isomorphic = nx.is_isomorphic(G1, G2)
+
+# Get isomorphism mapping
+from networkx.algorithms import isomorphism
+GM = isomorphism.GraphMatcher(G1, G2)
+if GM.is_isomorphic():
+    mapping = GM.mapping
+```
+
+### Subgraph Isomorphism
+```python
+# Check if G1 is subgraph isomorphic to G2
+is_subgraph_iso = nx.is_isomorphic(G1, G2.subgraph(nodes))
+```
+
+## Traversal Algorithms
+
+### Depth-First Search (DFS)
+```python
+# DFS edges
+dfs_edges = list(nx.dfs_edges(G, source=1))
+
+# DFS tree
+dfs_tree = nx.dfs_tree(G, source=1)
+
+# DFS predecessors
+dfs_pred = nx.dfs_predecessors(G, source=1)
+
+# Preorder and postorder
+preorder = list(nx.dfs_preorder_nodes(G, source=1))
+postorder = list(nx.dfs_postorder_nodes(G, source=1))
+```
+
+### Breadth-First Search (BFS)
+```python
+# BFS edges
+bfs_edges = list(nx.bfs_edges(G, source=1))
+
+# BFS tree
+bfs_tree = nx.bfs_tree(G, source=1)
+
+# BFS predecessors and successors
+bfs_pred = nx.bfs_predecessors(G, source=1)
+bfs_succ = nx.bfs_successors(G, source=1)
+```
+
+## Efficiency Considerations
+
+### Algorithm Complexity
+- Many algorithms have parameters to control computation time
+- For large graphs, consider approximate algorithms
+- Use `k` parameter to sample nodes in centrality calculations
+- Set `max_iter` for iterative algorithms
+
+### Memory Usage
+- Iterator-based functions (e.g., `nx.simple_cycles()`) save memory
+- Convert to list only when necessary
+- Use generators for large result sets
+
+### Numerical Precision
+When using weighted algorithms with floating-point numbers, results are approximate. Consider:
+- Using integer weights when possible
+- Setting appropriate tolerance parameters
+- Being aware of accumulated rounding errors in iterative algorithms

skills/networkx/references/generators.md

@@ -0,0 +1,378 @@
+# NetworkX Graph Generators
+
+## Classic Graphs
+
+### Complete Graphs
+```python
+# Complete graph (all nodes connected to all others)
+G = nx.complete_graph(n=10)
+
+# Complete bipartite graph
+G = nx.complete_bipartite_graph(n1=5, n2=7)
+
+# Complete multipartite graph
+G = nx.complete_multipartite_graph(3, 4, 5)  # Three partitions
+```
+
+### Cycle and Path Graphs
+```python
+# Cycle graph (nodes arranged in circle)
+G = nx.cycle_graph(n=20)
+
+# Path graph (linear chain)
+G = nx.path_graph(n=15)
+
+# Circular ladder graph
+G = nx.circular_ladder_graph(n=10)
+```
+
+### Regular Graphs
+```python
+# Empty graph (no edges)
+G = nx.empty_graph(n=10)
+
+# Null graph (no nodes)
+G = nx.null_graph()
+
+# Star graph (one central node connected to all others)
+G = nx.star_graph(n=19)  # Creates 20-node star
+
+# Wheel graph (cycle with central hub)
+G = nx.wheel_graph(n=10)
+```
+
+### Special Named Graphs
+```python
+# Bull graph
+G = nx.bull_graph()
+
+# Chvatal graph
+G = nx.chvatal_graph()
+
+# Cubical graph
+G = nx.cubical_graph()
+
+# Diamond graph
+G = nx.diamond_graph()
+
+# Dodecahedral graph
+G = nx.dodecahedral_graph()
+
+# Heawood graph
+G = nx.heawood_graph()
+
+# House graph
+G = nx.house_graph()
+
+# Petersen graph
+G = nx.petersen_graph()
+
+# Karate club graph (classic social network)
+G = nx.karate_club_graph()
+```
+
+## Random Graphs
+
+### Erdős-Rényi Graphs
+```python
+# G(n, p) model: n nodes, edge probability p
+G = nx.erdos_renyi_graph(n=100, p=0.1, seed=42)
+
+# G(n, m) model: n nodes, exactly m edges
+G = nx.gnm_random_graph(n=100, m=500, seed=42)
+
+# Fast version (for large sparse graphs)
+G = nx.fast_gnp_random_graph(n=10000, p=0.0001, seed=42)
+```
+
+### Watts-Strogatz Small-World
+```python
+# Small-world network with rewiring
+# n nodes, k nearest neighbors, rewiring probability p
+G = nx.watts_strogatz_graph(n=100, k=6, p=0.1, seed=42)
+
+# Connected version (guarantees connectivity)
+G = nx.connected_watts_strogatz_graph(n=100, k=6, p=0.1, tries=100, seed=42)
+```
+
+### Barabási-Albert Preferential Attachment
+```python
+# Scale-free network (power-law degree distribution)
+# n nodes, m edges to attach from new node
+G = nx.barabasi_albert_graph(n=100, m=3, seed=42)
+
+# Extended version with parameters
+G = nx.extended_barabasi_albert_graph(n=100, m=3, p=0.5, q=0.2, seed=42)
+```
+
+### Power Law Degree Sequence
+```python
+# Power law cluster graph
+G = nx.powerlaw_cluster_graph(n=100, m=3, p=0.1, seed=42)
+
+# Random power law tree
+G = nx.random_powerlaw_tree(n=100, gamma=3, seed=42, tries=1000)
+```
+
+### Configuration Model
+```python
+# Graph with specified degree sequence
+degree_sequence = [3, 3, 3, 3, 2, 2, 2, 1, 1, 1]
+G = nx.configuration_model(degree_sequence, seed=42)
+
+# Remove self-loops and parallel edges
+G = nx.Graph(G)
+G.remove_edges_from(nx.selfloop_edges(G))
+```
+
+### Random Geometric Graphs
+```python
+# Nodes in unit square, edges if distance < radius
+G = nx.random_geometric_graph(n=100, radius=0.2, seed=42)
+
+# With positions
+pos = nx.get_node_attributes(G, 'pos')
+```
+
+### Random Regular Graphs
+```python
+# Every node has exactly d neighbors
+G = nx.random_regular_graph(d=3, n=100, seed=42)
+```
+
+### Stochastic Block Model
+```python
+# Community structure model
+sizes = [50, 50, 50]  # Three communities
+probs = [[0.25, 0.05, 0.02],  # Within and between community probabilities
+         [0.05, 0.35, 0.07],
+         [0.02, 0.07, 0.40]]
+G = nx.stochastic_block_model(sizes, probs, seed=42)
+```
+
+## Lattice and Grid Graphs
+
+### Grid Graphs
+```python
+# 2D grid
+G = nx.grid_2d_graph(m=5, n=7)  # 5x7 grid
+
+# 3D grid
+G = nx.grid_graph(dim=[5, 7, 3])  # 5x7x3 grid
+
+# Hexagonal lattice
+G = nx.hexagonal_lattice_graph(m=5, n=7)
+
+# Triangular lattice
+G = nx.triangular_lattice_graph(m=5, n=7)
+```
+
+### Hypercube
+```python
+# n-dimensional hypercube
+G = nx.hypercube_graph(n=4)
+```
+
+## Tree Graphs
+
+### Random Trees
+```python
+# Random tree with n nodes
+G = nx.random_tree(n=100, seed=42)
+
+# Prefix tree (tries)
+G = nx.prefix_tree([[0, 1, 2], [0, 1, 3], [0, 4]])
+```
+
+### Balanced Trees
+```python
+# Balanced r-ary tree of height h
+G = nx.balanced_tree(r=2, h=5)  # Binary tree, height 5
+
+# Full r-ary tree with n nodes
+G = nx.full_rary_tree(r=3, n=100)  # Ternary tree
+```
+
+### Barbell and Lollipop Graphs
+```python
+# Two complete graphs connected by path
+G = nx.barbell_graph(m1=5, m2=3)  # Two K_5 graphs with 3-node path
+
+# Complete graph connected to path
+G = nx.lollipop_graph(m=7, n=5)  # K_7 with 5-node path
+```
+
+## Social Network Models
+
+### Karate Club
+```python
+# Zachary's karate club (classic social network)
+G = nx.karate_club_graph()
+```
+
+### Davis Southern Women
+```python
+# Bipartite social network
+G = nx.davis_southern_women_graph()
+```
+
+### Florentine Families
+```python
+# Historical marriage and business networks
+G = nx.florentine_families_graph()
+```
+
+### Les Misérables
+```python
+# Character co-occurrence network
+G = nx.les_miserables_graph()
+```
+
+## Directed Graph Generators
+
+### Random Directed Graphs
+```python
+# Directed Erdős-Rényi
+G = nx.gnp_random_graph(n=100, p=0.1, directed=True, seed=42)
+
+# Scale-free directed
+G = nx.scale_free_graph(n=100, seed=42)
+```
+
+### DAG (Directed Acyclic Graph)
+```python
+# Random DAG
+G = nx.gnp_random_graph(n=20, p=0.2, directed=True, seed=42)
+G = nx.DiGraph([(u, v) for (u, v) in G.edges() if u < v])  # Remove backward edges
+```
+
+### Tournament Graphs
+```python
+# Random tournament (complete directed graph)
+G = nx.random_tournament(n=10, seed=42)
+```
+
+## Duplication-Divergence Models
+
+### Duplication Divergence Graph
+```python
+# Biological network model (protein interaction networks)
+G = nx.duplication_divergence_graph(n=100, p=0.5, seed=42)
+```
+
+## Degree Sequence Generators
+
+### Valid Degree Sequences
+```python
+# Check if degree sequence is valid (graphical)
+sequence = [3, 3, 3, 3, 2, 2, 2, 1, 1, 1]
+is_valid = nx.is_graphical(sequence)
+
+# For directed graphs
+in_sequence = [2, 2, 2, 1, 1]
+out_sequence = [2, 2, 1, 2, 1]
+is_valid = nx.is_digraphical(in_sequence, out_sequence)
+```
+
+### Creating from Degree Sequence
+```python
+# Havel-Hakimi algorithm
+G = nx.havel_hakimi_graph(degree_sequence)
+
+# Configuration model (allows multi-edges/self-loops)
+G = nx.configuration_model(degree_sequence)
+
+# Directed configuration model
+G = nx.directed_configuration_model(in_degree_sequence, out_degree_sequence)
+```
+
+## Bipartite Graphs
+
+### Random Bipartite
+```python
+# Random bipartite with two node sets
+G = nx.bipartite.random_graph(n=50, m=30, p=0.1, seed=42)
+
+# Configuration model for bipartite
+G = nx.bipartite.configuration_model(deg1=[3, 3, 2], deg2=[2, 2, 2, 2], seed=42)
+```
+
+### Bipartite Generators
+```python
+# Complete bipartite
+G = nx.complete_bipartite_graph(n1=5, n2=7)
+
+# Gnmk random bipartite (n, m nodes, k edges)
+G = nx.bipartite.gnmk_random_graph(n=10, m=8, k=20, seed=42)
+```
+
+## Operators on Graphs
+
+### Graph Operations
+```python
+# Union
+G = nx.union(G1, G2)
+
+# Disjoint union
+G = nx.disjoint_union(G1, G2)
+
+# Compose (overlay)
+G = nx.compose(G1, G2)
+
+# Complement
+G = nx.complement(G1)
+
+# Cartesian product
+G = nx.cartesian_product(G1, G2)
+
+# Tensor (Kronecker) product
+G = nx.tensor_product(G1, G2)
+
+# Strong product
+G = nx.strong_product(G1, G2)
+```
+
+## Customization and Seeding
+
+### Setting Random Seed
+Always set seed for reproducible graphs:
+```python
+G = nx.erdos_renyi_graph(n=100, p=0.1, seed=42)
+```
+
+### Converting Graph Types
+```python
+# Convert to specific type
+G_directed = G.to_directed()
+G_undirected = G.to_undirected()
+G_multi = nx.MultiGraph(G)
+```
+
+## Performance Considerations
+
+### Fast Generators
+For large graphs, use optimized generators:
+```python
+# Fast ER graph (sparse)
+G = nx.fast_gnp_random_graph(n=10000, p=0.0001, seed=42)
+```
+
+### Memory Efficiency
+Some generators create graphs incrementally to save memory. For very large graphs, consider:
+- Using sparse representations
+- Generating subgraphs as needed
+- Working with adjacency lists or edge lists instead of full graphs
+
+## Validation and Properties
+
+### Checking Generated Graphs
+```python
+# Verify properties
+print(f"Nodes: {G.number_of_nodes()}")
+print(f"Edges: {G.number_of_edges()}")
+print(f"Density: {nx.density(G)}")
+print(f"Connected: {nx.is_connected(G)}")
+
+# Degree distribution
+degree_sequence = sorted([d for n, d in G.degree()], reverse=True)
+```

skills/networkx/references/graph-basics.md

@@ -0,0 +1,283 @@
+# NetworkX Graph Basics
+
+## Graph Types
+
+NetworkX supports four main graph classes:
+
+### Graph (Undirected)
+```python
+import networkx as nx
+G = nx.Graph()
+```
+- Undirected graphs with single edges between nodes
+- No parallel edges allowed
+- Edges are bidirectional
+
+### DiGraph (Directed)
+```python
+G = nx.DiGraph()
+```
+- Directed graphs with one-way connections
+- Edge direction matters: (u, v) ≠ (v, u)
+- Used for modeling directed relationships
+
+### MultiGraph (Undirected Multi-edge)
+```python
+G = nx.MultiGraph()
+```
+- Allows multiple edges between same node pairs
+- Useful for modeling multiple relationships
+
+### MultiDiGraph (Directed Multi-edge)
+```python
+G = nx.MultiDiGraph()
+```
+- Directed graph with multiple edges between nodes
+- Combines features of DiGraph and MultiGraph
+
+## Creating and Adding Nodes
+
+### Single Node Addition
+```python
+G.add_node(1)
+G.add_node("protein_A")
+G.add_node((x, y))  # Nodes can be any hashable type
+```
+
+### Bulk Node Addition
+```python
+G.add_nodes_from([2, 3, 4])
+G.add_nodes_from(range(100, 110))
+```
+
+### Nodes with Attributes
+```python
+G.add_node(1, time='5pm', color='red')
+G.add_nodes_from([
+    (4, {"color": "red"}),
+    (5, {"color": "blue", "weight": 1.5})
+])
+```
+
+### Important Node Properties
+- Nodes can be any hashable Python object: strings, tuples, numbers, custom objects
+- Node attributes stored as key-value pairs
+- Use meaningful node identifiers for clarity
+
+## Creating and Adding Edges
+
+### Single Edge Addition
+```python
+G.add_edge(1, 2)
+G.add_edge('gene_A', 'gene_B')
+```
+
+### Bulk Edge Addition
+```python
+G.add_edges_from([(1, 2), (1, 3), (2, 4)])
+G.add_edges_from(edge_list)
+```
+
+### Edges with Attributes
+```python
+G.add_edge(1, 2, weight=4.7, relation='interacts')
+G.add_edges_from([
+    (1, 2, {'weight': 4.7}),
+    (2, 3, {'weight': 8.2, 'color': 'blue'})
+])
+```
+
+### Adding from Edge List with Attributes
+```python
+# From pandas DataFrame
+import pandas as pd
+df = pd.DataFrame({'source': [1, 2], 'target': [2, 3], 'weight': [4.7, 8.2]})
+G = nx.from_pandas_edgelist(df, 'source', 'target', edge_attr='weight')
+```
+
+## Examining Graph Structure
+
+### Basic Properties
+```python
+# Get collections
+G.nodes              # NodeView of all nodes
+G.edges              # EdgeView of all edges
+G.adj                # AdjacencyView for neighbor relationships
+
+# Count elements
+G.number_of_nodes()  # Total node count
+G.number_of_edges()  # Total edge count
+len(G)              # Number of nodes (shorthand)
+
+# Degree information
+G.degree()          # DegreeView of all node degrees
+G.degree(1)         # Degree of specific node
+list(G.degree())    # List of (node, degree) pairs
+```
+
+### Checking Existence
+```python
+# Check if node exists
+1 in G              # Returns True/False
+G.has_node(1)
+
+# Check if edge exists
+G.has_edge(1, 2)
+```
+
+### Accessing Neighbors
+```python
+# Get neighbors of node 1
+list(G.neighbors(1))
+list(G[1])          # Dictionary-like access
+
+# For directed graphs
+list(G.predecessors(1))  # Incoming edges
+list(G.successors(1))    # Outgoing edges
+```
+
+### Iterating Over Elements
+```python
+# Iterate over nodes
+for node in G.nodes:
+    print(node, G.nodes[node])  # Access node attributes
+
+# Iterate over edges
+for u, v in G.edges:
+    print(u, v, G[u][v])  # Access edge attributes
+
+# Iterate with attributes
+for node, attrs in G.nodes(data=True):
+    print(node, attrs)
+
+for u, v, attrs in G.edges(data=True):
+    print(u, v, attrs)
+```
+
+## Modifying Graphs
+
+### Removing Elements
+```python
+# Remove single node (also removes incident edges)
+G.remove_node(1)
+
+# Remove multiple nodes
+G.remove_nodes_from([1, 2, 3])
+
+# Remove edges
+G.remove_edge(1, 2)
+G.remove_edges_from([(1, 2), (2, 3)])
+```
+
+### Clearing Graph
+```python
+G.clear()           # Remove all nodes and edges
+G.clear_edges()     # Remove only edges, keep nodes
+```
+
+## Attributes and Metadata
+
+### Graph-Level Attributes
+```python
+G.graph['name'] = 'Social Network'
+G.graph['date'] = '2025-01-15'
+print(G.graph)
+```
+
+### Node Attributes
+```python
+# Set at creation
+G.add_node(1, time='5pm', weight=0.5)
+
+# Set after creation
+G.nodes[1]['time'] = '6pm'
+nx.set_node_attributes(G, {1: 'red', 2: 'blue'}, 'color')
+
+# Get attributes
+G.nodes[1]
+G.nodes[1]['time']
+nx.get_node_attributes(G, 'color')
+```
+
+### Edge Attributes
+```python
+# Set at creation
+G.add_edge(1, 2, weight=4.7, color='red')
+
+# Set after creation
+G[1][2]['weight'] = 5.0
+nx.set_edge_attributes(G, {(1, 2): 10.5}, 'weight')
+
+# Get attributes
+G[1][2]
+G[1][2]['weight']
+G.edges[1, 2]
+nx.get_edge_attributes(G, 'weight')
+```
+
+## Subgraphs and Views
+
+### Subgraph Creation
+```python
+# Create subgraph from node list
+nodes_subset = [1, 2, 3, 4]
+H = G.subgraph(nodes_subset)  # Returns view (references original)
+
+# Create independent copy
+H = G.subgraph(nodes_subset).copy()
+
+# Edge-induced subgraph
+edge_subset = [(1, 2), (2, 3)]
+H = G.edge_subgraph(edge_subset)
+```
+
+### Graph Views
+```python
+# Reverse view (for directed graphs)
+G_reversed = G.reverse()
+
+# Convert between directed/undirected
+G_undirected = G.to_undirected()
+G_directed = G.to_directed()
+```
+
+## Graph Information and Diagnostics
+
+### Basic Information
+```python
+print(nx.info(G))   # Summary of graph structure
+
+# Density (ratio of actual edges to possible edges)
+nx.density(G)
+
+# Check if graph is directed
+G.is_directed()
+
+# Check if graph is multigraph
+G.is_multigraph()
+```
+
+### Connectivity Checks
+```python
+# For undirected graphs
+nx.is_connected(G)
+nx.number_connected_components(G)
+
+# For directed graphs
+nx.is_strongly_connected(G)
+nx.is_weakly_connected(G)
+```
+
+## Important Considerations
+
+### Floating Point Precision
+Once graphs contain floating point numbers, all results are inherently approximate due to precision limitations. Small arithmetic errors can affect algorithm outcomes, particularly in minimum/maximum computations.
+
+### Memory Considerations
+Each time a script starts, graph data must be loaded into memory. For large datasets, this can cause performance issues. Consider:
+- Using efficient data formats (pickle for Python objects)
+- Loading only necessary subgraphs
+- Using graph databases for very large networks
+
+### Node and Edge Removal Behavior
+When a node is removed, all edges incident with that node are automatically removed as well.

skills/networkx/references/io.md

@@ -0,0 +1,441 @@
+# NetworkX Input/Output
+
+## Reading Graphs from Files
+
+### Adjacency List Format
+```python
+# Read adjacency list (simple text format)
+G = nx.read_adjlist('graph.adjlist')
+
+# With node type conversion
+G = nx.read_adjlist('graph.adjlist', nodetype=int)
+
+# For directed graphs
+G = nx.read_adjlist('graph.adjlist', create_using=nx.DiGraph())
+
+# Write adjacency list
+nx.write_adjlist(G, 'graph.adjlist')
+```
+
+Example adjacency list format:
+```
+# node neighbors
+0 1 2
+1 0 3 4
+2 0 3
+3 1 2 4
+4 1 3
+```
+
+### Edge List Format
+```python
+# Read edge list
+G = nx.read_edgelist('graph.edgelist')
+
+# With node types and edge data
+G = nx.read_edgelist('graph.edgelist',
+                     nodetype=int,
+                     data=(('weight', float),))
+
+# Read weighted edge list
+G = nx.read_weighted_edgelist('weighted.edgelist')
+
+# Write edge list
+nx.write_edgelist(G, 'graph.edgelist')
+
+# Write weighted edge list
+nx.write_weighted_edgelist(G, 'weighted.edgelist')
+```
+
+Example edge list format:
+```
+# source target
+0 1
+1 2
+2 3
+3 0
+```
+
+Example weighted edge list:
+```
+# source target weight
+0 1 0.5
+1 2 1.0
+2 3 0.75
+```
+
+### GML (Graph Modelling Language)
+```python
+# Read GML (preserves all attributes)
+G = nx.read_gml('graph.gml')
+
+# Write GML
+nx.write_gml(G, 'graph.gml')
+```
+
+### GraphML Format
+```python
+# Read GraphML (XML-based format)
+G = nx.read_graphml('graph.graphml')
+
+# Write GraphML
+nx.write_graphml(G, 'graph.graphml')
+
+# With specific encoding
+nx.write_graphml(G, 'graph.graphml', encoding='utf-8')
+```
+
+### GEXF (Graph Exchange XML Format)
+```python
+# Read GEXF
+G = nx.read_gexf('graph.gexf')
+
+# Write GEXF
+nx.write_gexf(G, 'graph.gexf')
+```
+
+### Pajek Format
+```python
+# Read Pajek .net files
+G = nx.read_pajek('graph.net')
+
+# Write Pajek format
+nx.write_pajek(G, 'graph.net')
+```
+
+### LEDA Format
+```python
+# Read LEDA format
+G = nx.read_leda('graph.leda')
+
+# Write LEDA format
+nx.write_leda(G, 'graph.leda')
+```
+
+## Working with Pandas
+
+### From Pandas DataFrame
+```python
+import pandas as pd
+
+# Create graph from edge list DataFrame
+df = pd.DataFrame({
+    'source': [1, 2, 3, 4],
+    'target': [2, 3, 4, 1],
+    'weight': [0.5, 1.0, 0.75, 0.25]
+})
+
+# Create graph
+G = nx.from_pandas_edgelist(df,
+                            source='source',
+                            target='target',
+                            edge_attr='weight')
+
+# With multiple edge attributes
+G = nx.from_pandas_edgelist(df,
+                            source='source',
+                            target='target',
+                            edge_attr=['weight', 'color', 'type'])
+
+# Create directed graph
+G = nx.from_pandas_edgelist(df,
+                            source='source',
+                            target='target',
+                            create_using=nx.DiGraph())
+```
+
+### To Pandas DataFrame
+```python
+# Convert graph to edge list DataFrame
+df = nx.to_pandas_edgelist(G)
+
+# With specific edge attributes
+df = nx.to_pandas_edgelist(G, source='node1', target='node2')
+```
+
+### Adjacency Matrix with Pandas
+```python
+# Create DataFrame from adjacency matrix
+df = nx.to_pandas_adjacency(G, dtype=int)
+
+# Create graph from adjacency DataFrame
+G = nx.from_pandas_adjacency(df)
+
+# For directed graphs
+G = nx.from_pandas_adjacency(df, create_using=nx.DiGraph())
+```
+
+## NumPy and SciPy Integration
+
+### Adjacency Matrix
+```python
+import numpy as np
+
+# To NumPy adjacency matrix
+A = nx.to_numpy_array(G, dtype=int)
+
+# With specific node order
+nodelist = [1, 2, 3, 4, 5]
+A = nx.to_numpy_array(G, nodelist=nodelist)
+
+# From NumPy array
+G = nx.from_numpy_array(A)
+
+# For directed graphs
+G = nx.from_numpy_array(A, create_using=nx.DiGraph())
+```
+
+### Sparse Matrix (SciPy)
+```python
+from scipy import sparse
+
+# To sparse matrix
+A = nx.to_scipy_sparse_array(G)
+
+# With specific format (csr, csc, coo, etc.)
+A_csr = nx.to_scipy_sparse_array(G, format='csr')
+
+# From sparse matrix
+G = nx.from_scipy_sparse_array(A)
+```
+
+## JSON Format
+
+### Node-Link Format
+```python
+import json
+
+# To node-link format (good for d3.js)
+data = nx.node_link_data(G)
+with open('graph.json', 'w') as f:
+    json.dump(data, f)
+
+# From node-link format
+with open('graph.json', 'r') as f:
+    data = json.load(f)
+G = nx.node_link_graph(data)
+```
+
+### Adjacency Data Format
+```python
+# To adjacency format
+data = nx.adjacency_data(G)
+with open('graph.json', 'w') as f:
+    json.dump(data, f)
+
+# From adjacency format
+with open('graph.json', 'r') as f:
+    data = json.load(f)
+G = nx.adjacency_graph(data)
+```
+
+### Tree Data Format
+```python
+# For tree graphs
+data = nx.tree_data(G, root=0)
+with open('tree.json', 'w') as f:
+    json.dump(data, f)
+
+# From tree format
+with open('tree.json', 'r') as f:
+    data = json.load(f)
+G = nx.tree_graph(data)
+```
+
+## Pickle Format
+
+### Binary Pickle
+```python
+import pickle
+
+# Write pickle (preserves all Python objects)
+with open('graph.pkl', 'wb') as f:
+    pickle.dump(G, f)
+
+# Read pickle
+with open('graph.pkl', 'rb') as f:
+    G = pickle.load(f)
+
+# NetworkX convenience functions
+nx.write_gpickle(G, 'graph.gpickle')
+G = nx.read_gpickle('graph.gpickle')
+```
+
+## CSV Files
+
+### Custom CSV Reading
+```python
+import csv
+
+# Read edges from CSV
+G = nx.Graph()
+with open('edges.csv', 'r') as f:
+    reader = csv.DictReader(f)
+    for row in reader:
+        G.add_edge(row['source'], row['target'], weight=float(row['weight']))
+
+# Write edges to CSV
+with open('edges.csv', 'w', newline='') as f:
+    writer = csv.writer(f)
+    writer.writerow(['source', 'target', 'weight'])
+    for u, v, data in G.edges(data=True):
+        writer.writerow([u, v, data.get('weight', 1.0)])
+```
+
+## Database Integration
+
+### SQL Databases
+```python
+import sqlite3
+import pandas as pd
+
+# Read from SQL database via pandas
+conn = sqlite3.connect('network.db')
+df = pd.read_sql_query("SELECT source, target, weight FROM edges", conn)
+G = nx.from_pandas_edgelist(df, 'source', 'target', edge_attr='weight')
+conn.close()
+
+# Write to SQL database
+df = nx.to_pandas_edgelist(G)
+conn = sqlite3.connect('network.db')
+df.to_sql('edges', conn, if_exists='replace', index=False)
+conn.close()
+```
+
+## Graph Formats for Visualization
+
+### DOT Format (Graphviz)
+```python
+# Write DOT file for Graphviz
+nx.drawing.nx_pydot.write_dot(G, 'graph.dot')
+
+# Read DOT file
+G = nx.drawing.nx_pydot.read_dot('graph.dot')
+
+# Generate directly to image (requires Graphviz)
+from networkx.drawing.nx_pydot import to_pydot
+pydot_graph = to_pydot(G)
+pydot_graph.write_png('graph.png')
+```
+
+## Cytoscape Integration
+
+### Cytoscape JSON
+```python
+# Export for Cytoscape
+data = nx.cytoscape_data(G)
+with open('cytoscape.json', 'w') as f:
+    json.dump(data, f)
+
+# Import from Cytoscape
+with open('cytoscape.json', 'r') as f:
+    data = json.load(f)
+G = nx.cytoscape_graph(data)
+```
+
+## Specialized Formats
+
+### Matrix Market Format
+```python
+from scipy.io import mmread, mmwrite
+
+# Read Matrix Market
+A = mmread('graph.mtx')
+G = nx.from_scipy_sparse_array(A)
+
+# Write Matrix Market
+A = nx.to_scipy_sparse_array(G)
+mmwrite('graph.mtx', A)
+```
+
+### Shapefile (for Geographic Networks)
+```python
+# Requires pyshp library
+# Read geographic network from shapefile
+G = nx.read_shp('roads.shp')
+
+# Write to shapefile
+nx.write_shp(G, 'network')
+```
+
+## Format Selection Guidelines
+
+### Choose Based on Requirements
+
+**Adjacency List** - Simple, human-readable, no attributes
+- Best for: Simple unweighted graphs, quick viewing
+
+**Edge List** - Simple, supports weights, human-readable
+- Best for: Weighted graphs, importing/exporting data
+
+**GML/GraphML** - Full attribute preservation, XML-based
+- Best for: Complete graph serialization with all metadata
+
+**JSON** - Web-friendly, JavaScript integration
+- Best for: Web applications, d3.js visualizations
+
+**Pickle** - Fast, preserves Python objects, binary
+- Best for: Python-only storage, complex attributes
+
+**Pandas** - Data analysis integration, DataFrame operations
+- Best for: Data processing pipelines, statistical analysis
+
+**NumPy/SciPy** - Numerical computation, sparse matrices
+- Best for: Matrix operations, scientific computing
+
+**DOT** - Visualization, Graphviz integration
+- Best for: Creating visual diagrams
+
+## Performance Considerations
+
+### Large Graphs
+For large graphs, consider:
+```python
+# Use compressed formats
+import gzip
+with gzip.open('graph.adjlist.gz', 'wt') as f:
+    nx.write_adjlist(G, f)
+
+with gzip.open('graph.adjlist.gz', 'rt') as f:
+    G = nx.read_adjlist(f)
+
+# Use binary formats (faster)
+nx.write_gpickle(G, 'graph.gpickle')  # Faster than text formats
+
+# Use sparse matrices for adjacency
+A = nx.to_scipy_sparse_array(G, format='csr')  # Memory efficient
+```
+
+### Incremental Loading
+For very large graphs:
+```python
+# Load graph incrementally from edge list
+G = nx.Graph()
+with open('huge_graph.edgelist') as f:
+    for line in f:
+        u, v = line.strip().split()
+        G.add_edge(u, v)
+
+        # Process in chunks
+        if G.number_of_edges() % 100000 == 0:
+            print(f"Loaded {G.number_of_edges()} edges")
+```
+
+## Error Handling
+
+### Robust File Reading
+```python
+try:
+    G = nx.read_graphml('graph.graphml')
+except nx.NetworkXError as e:
+    print(f"Error reading GraphML: {e}")
+except FileNotFoundError:
+    print("File not found")
+    G = nx.Graph()
+
+# Check if file format is supported
+if os.path.exists('graph.txt'):
+    with open('graph.txt') as f:
+        first_line = f.readline()
+        # Detect format and read accordingly
+```

skills/networkx/references/visualization.md

@@ -0,0 +1,529 @@
+# NetworkX Graph Visualization
+
+## Basic Drawing with Matplotlib
+
+### Simple Visualization
+```python
+import networkx as nx
+import matplotlib.pyplot as plt
+
+# Create and draw graph
+G = nx.karate_club_graph()
+nx.draw(G)
+plt.show()
+
+# Save to file
+nx.draw(G)
+plt.savefig('graph.png', dpi=300, bbox_inches='tight')
+plt.close()
+```
+
+### Drawing with Labels
+```python
+# Draw with node labels
+nx.draw(G, with_labels=True)
+plt.show()
+
+# Custom labels
+labels = {i: f"Node {i}" for i in G.nodes()}
+nx.draw(G, labels=labels, with_labels=True)
+plt.show()
+```
+
+## Layout Algorithms
+
+### Spring Layout (Force-Directed)
+```python
+# Fruchterman-Reingold force-directed algorithm
+pos = nx.spring_layout(G, seed=42)
+nx.draw(G, pos=pos, with_labels=True)
+plt.show()
+
+# With parameters
+pos = nx.spring_layout(G, k=0.5, iterations=50, seed=42)
+```
+
+### Circular Layout
+```python
+# Arrange nodes in circle
+pos = nx.circular_layout(G)
+nx.draw(G, pos=pos, with_labels=True)
+plt.show()
+```
+
+### Random Layout
+```python
+# Random positioning
+pos = nx.random_layout(G, seed=42)
+nx.draw(G, pos=pos, with_labels=True)
+plt.show()
+```
+
+### Shell Layout
+```python
+# Concentric circles
+pos = nx.shell_layout(G)
+nx.draw(G, pos=pos, with_labels=True)
+plt.show()
+
+# With custom shells
+shells = [[0, 1, 2], [3, 4, 5, 6], [7, 8, 9]]
+pos = nx.shell_layout(G, nlist=shells)
+```
+
+### Spectral Layout
+```python
+# Use eigenvectors of graph Laplacian
+pos = nx.spectral_layout(G)
+nx.draw(G, pos=pos, with_labels=True)
+plt.show()
+```
+
+### Kamada-Kawai Layout
+```python
+# Energy-based layout
+pos = nx.kamada_kawai_layout(G)
+nx.draw(G, pos=pos, with_labels=True)
+plt.show()
+```
+
+### Planar Layout
+```python
+# For planar graphs only
+if nx.is_planar(G):
+    pos = nx.planar_layout(G)
+    nx.draw(G, pos=pos, with_labels=True)
+    plt.show()
+```
+
+### Tree Layouts
+```python
+# For tree graphs
+if nx.is_tree(G):
+    pos = nx.nx_agraph.graphviz_layout(G, prog='dot')
+    nx.draw(G, pos=pos, with_labels=True)
+    plt.show()
+```
+
+## Customizing Node Appearance
+
+### Node Colors
+```python
+# Single color
+nx.draw(G, node_color='red')
+
+# Different colors per node
+node_colors = ['red' if G.degree(n) > 5 else 'blue' for n in G.nodes()]
+nx.draw(G, node_color=node_colors)
+
+# Color by attribute
+colors = [G.nodes[n].get('value', 0) for n in G.nodes()]
+nx.draw(G, node_color=colors, cmap=plt.cm.viridis)
+plt.colorbar()
+plt.show()
+```
+
+### Node Sizes
+```python
+# Size by degree
+node_sizes = [100 * G.degree(n) for n in G.nodes()]
+nx.draw(G, node_size=node_sizes)
+
+# Size by centrality
+centrality = nx.degree_centrality(G)
+node_sizes = [3000 * centrality[n] for n in G.nodes()]
+nx.draw(G, node_size=node_sizes)
+```
+
+### Node Shapes
+```python
+# Draw nodes separately with different shapes
+pos = nx.spring_layout(G)
+
+# Circle nodes
+nx.draw_networkx_nodes(G, pos, nodelist=[0, 1, 2],
+                       node_shape='o', node_color='red')
+
+# Square nodes
+nx.draw_networkx_nodes(G, pos, nodelist=[3, 4, 5],
+                       node_shape='s', node_color='blue')
+
+nx.draw_networkx_edges(G, pos)
+nx.draw_networkx_labels(G, pos)
+plt.show()
+```
+
+### Node Borders
+```python
+nx.draw(G, pos=pos,
+        node_color='lightblue',
+        edgecolors='black',  # Node border color
+        linewidths=2)        # Node border width
+plt.show()
+```
+
+## Customizing Edge Appearance
+
+### Edge Colors
+```python
+# Single color
+nx.draw(G, edge_color='gray')
+
+# Different colors per edge
+edge_colors = ['red' if G[u][v].get('weight', 1) > 0.5 else 'blue'
+               for u, v in G.edges()]
+nx.draw(G, edge_color=edge_colors)
+
+# Color by weight
+edges = G.edges()
+weights = [G[u][v].get('weight', 1) for u, v in edges]
+nx.draw(G, edge_color=weights, edge_cmap=plt.cm.Reds)
+```
+
+### Edge Widths
+```python
+# Width by weight
+edge_widths = [3 * G[u][v].get('weight', 1) for u, v in G.edges()]
+nx.draw(G, width=edge_widths)
+
+# Width by betweenness
+edge_betweenness = nx.edge_betweenness_centrality(G)
+edge_widths = [5 * edge_betweenness[(u, v)] for u, v in G.edges()]
+nx.draw(G, width=edge_widths)
+```
+
+### Edge Styles
+```python
+# Dashed edges
+nx.draw(G, style='dashed')
+
+# Different styles per edge
+pos = nx.spring_layout(G)
+strong_edges = [(u, v) for u, v in G.edges() if G[u][v].get('weight', 0) > 0.5]
+weak_edges = [(u, v) for u, v in G.edges() if G[u][v].get('weight', 0) <= 0.5]
+
+nx.draw_networkx_nodes(G, pos)
+nx.draw_networkx_edges(G, pos, edgelist=strong_edges, style='solid', width=2)
+nx.draw_networkx_edges(G, pos, edgelist=weak_edges, style='dashed', width=1)
+plt.show()
+```
+
+### Directed Graphs (Arrows)
+```python
+# Draw directed graph with arrows
+G_directed = nx.DiGraph([(1, 2), (2, 3), (3, 1)])
+pos = nx.spring_layout(G_directed)
+
+nx.draw(G_directed, pos=pos, with_labels=True,
+        arrows=True,
+        arrowsize=20,
+        arrowstyle='->',
+        connectionstyle='arc3,rad=0.1')
+plt.show()
+```
+
+## Labels and Annotations
+
+### Node Labels
+```python
+pos = nx.spring_layout(G)
+
+# Custom labels
+labels = {n: f"N{n}" for n in G.nodes()}
+nx.draw_networkx_labels(G, pos, labels=labels, font_size=12, font_color='white')
+
+# Font customization
+nx.draw_networkx_labels(G, pos,
+                       font_size=10,
+                       font_family='serif',
+                       font_weight='bold')
+```
+
+### Edge Labels
+```python
+pos = nx.spring_layout(G)
+nx.draw_networkx_nodes(G, pos)
+nx.draw_networkx_edges(G, pos)
+
+# Edge labels from attributes
+edge_labels = nx.get_edge_attributes(G, 'weight')
+nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)
+plt.show()
+
+# Custom edge labels
+edge_labels = {(u, v): f"{u}-{v}" for u, v in G.edges()}
+nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)
+```
+
+## Advanced Drawing Techniques
+
+### Combining Draw Functions
+```python
+# Full control by separating components
+pos = nx.spring_layout(G, seed=42)
+
+# Draw edges
+nx.draw_networkx_edges(G, pos, alpha=0.3, width=1)
+
+# Draw nodes
+nx.draw_networkx_nodes(G, pos,
+                       node_color='lightblue',
+                       node_size=500,
+                       edgecolors='black')
+
+# Draw labels
+nx.draw_networkx_labels(G, pos, font_size=10)
+
+# Remove axis
+plt.axis('off')
+plt.tight_layout()
+plt.show()
+```
+
+### Subgraph Highlighting
+```python
+pos = nx.spring_layout(G)
+
+# Identify subgraph to highlight
+subgraph_nodes = [1, 2, 3, 4]
+subgraph = G.subgraph(subgraph_nodes)
+
+# Draw main graph
+nx.draw_networkx_nodes(G, pos, node_color='lightgray', node_size=300)
+nx.draw_networkx_edges(G, pos, alpha=0.2)
+
+# Highlight subgraph
+nx.draw_networkx_nodes(subgraph, pos, node_color='red', node_size=500)
+nx.draw_networkx_edges(subgraph, pos, edge_color='red', width=2)
+
+nx.draw_networkx_labels(G, pos)
+plt.axis('off')
+plt.show()
+```
+
+### Community Coloring
+```python
+from networkx.algorithms import community
+
+# Detect communities
+communities = community.greedy_modularity_communities(G)
+
+# Assign colors
+color_map = {}
+colors = ['red', 'blue', 'green', 'yellow', 'purple', 'orange']
+for i, comm in enumerate(communities):
+    for node in comm:
+        color_map[node] = colors[i % len(colors)]
+
+node_colors = [color_map[n] for n in G.nodes()]
+
+pos = nx.spring_layout(G)
+nx.draw(G, pos=pos, node_color=node_colors, with_labels=True)
+plt.show()
+```
+
+## Creating Publication-Quality Figures
+
+### High Resolution Export
+```python
+plt.figure(figsize=(12, 8))
+pos = nx.spring_layout(G, seed=42)
+
+nx.draw(G, pos=pos,
+        node_color='lightblue',
+        node_size=500,
+        edge_color='gray',
+        width=1,
+        with_labels=True,
+        font_size=10)
+
+plt.title('Graph Visualization', fontsize=16)
+plt.axis('off')
+plt.tight_layout()
+plt.savefig('publication_graph.png', dpi=300, bbox_inches='tight')
+plt.savefig('publication_graph.pdf', bbox_inches='tight')  # Vector format
+plt.close()
+```
+
+### Multi-Panel Figures
+```python
+fig, axes = plt.subplots(1, 3, figsize=(18, 6))
+
+# Different layouts
+layouts = [nx.circular_layout(G), nx.spring_layout(G), nx.spectral_layout(G)]
+titles = ['Circular', 'Spring', 'Spectral']
+
+for ax, pos, title in zip(axes, layouts, titles):
+    nx.draw(G, pos=pos, ax=ax, with_labels=True, node_color='lightblue')
+    ax.set_title(title)
+    ax.axis('off')
+
+plt.tight_layout()
+plt.savefig('layouts_comparison.png', dpi=300)
+plt.close()
+```
+
+## Interactive Visualization Libraries
+
+### Plotly (Interactive)
+```python
+import plotly.graph_objects as go
+
+# Create positions
+pos = nx.spring_layout(G)
+
+# Edge trace
+edge_x = []
+edge_y = []
+for edge in G.edges():
+    x0, y0 = pos[edge[0]]
+    x1, y1 = pos[edge[1]]
+    edge_x.extend([x0, x1, None])
+    edge_y.extend([y0, y1, None])
+
+edge_trace = go.Scatter(
+    x=edge_x, y=edge_y,
+    line=dict(width=0.5, color='#888'),
+    hoverinfo='none',
+    mode='lines')
+
+# Node trace
+node_x = [pos[node][0] for node in G.nodes()]
+node_y = [pos[node][1] for node in G.nodes()]
+
+node_trace = go.Scatter(
+    x=node_x, y=node_y,
+    mode='markers',
+    hoverinfo='text',
+    marker=dict(
+        showscale=True,
+        colorscale='YlGnBu',
+        size=10,
+        colorbar=dict(thickness=15, title='Node Connections'),
+        line_width=2))
+
+# Color by degree
+node_adjacencies = [len(list(G.neighbors(node))) for node in G.nodes()]
+node_trace.marker.color = node_adjacencies
+
+fig = go.Figure(data=[edge_trace, node_trace],
+                layout=go.Layout(
+                    showlegend=False,
+                    hovermode='closest',
+                    margin=dict(b=0, l=0, r=0, t=0)))
+
+fig.show()
+```
+
+### PyVis (Interactive HTML)
+```python
+from pyvis.network import Network
+
+# Create network
+net = Network(notebook=True, height='750px', width='100%')
+
+# Add nodes and edges from NetworkX
+net.from_nx(G)
+
+# Customize
+net.show_buttons(filter_=['physics'])
+
+# Save
+net.show('graph.html')
+```
+
+### Graphviz (via pydot)
+```python
+# Requires graphviz and pydot
+from networkx.drawing.nx_pydot import graphviz_layout
+
+pos = graphviz_layout(G, prog='neato')  # neato, dot, fdp, sfdp, circo, twopi
+nx.draw(G, pos=pos, with_labels=True)
+plt.show()
+
+# Export to graphviz
+nx.drawing.nx_pydot.write_dot(G, 'graph.dot')
+```
+
+## Bipartite Graph Visualization
+
+### Two-Set Layout
+```python
+from networkx.algorithms import bipartite
+
+# Create bipartite graph
+B = nx.Graph()
+B.add_nodes_from([1, 2, 3, 4], bipartite=0)
+B.add_nodes_from(['a', 'b', 'c', 'd', 'e'], bipartite=1)
+B.add_edges_from([(1, 'a'), (1, 'b'), (2, 'b'), (2, 'c'), (3, 'd'), (4, 'e')])
+
+# Layout with two columns
+pos = {}
+top_nodes = [n for n, d in B.nodes(data=True) if d['bipartite'] == 0]
+bottom_nodes = [n for n, d in B.nodes(data=True) if d['bipartite'] == 1]
+
+pos.update({node: (0, i) for i, node in enumerate(top_nodes)})
+pos.update({node: (1, i) for i, node in enumerate(bottom_nodes)})
+
+nx.draw(B, pos=pos, with_labels=True,
+        node_color=['lightblue' if B.nodes[n]['bipartite'] == 0 else 'lightgreen'
+                   for n in B.nodes()])
+plt.show()
+```
+
+## 3D Visualization
+
+### 3D Network Plot
+```python
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+
+# 3D spring layout
+pos = nx.spring_layout(G, dim=3, seed=42)
+
+# Extract coordinates
+node_xyz = np.array([pos[v] for v in G.nodes()])
+edge_xyz = np.array([(pos[u], pos[v]) for u, v in G.edges()])
+
+# Create figure
+fig = plt.figure(figsize=(10, 8))
+ax = fig.add_subplot(111, projection='3d')
+
+# Plot edges
+for vizedge in edge_xyz:
+    ax.plot(*vizedge.T, color='gray', alpha=0.5)
+
+# Plot nodes
+ax.scatter(*node_xyz.T, s=100, c='lightblue', edgecolors='black')
+
+# Labels
+for i, (x, y, z) in enumerate(node_xyz):
+    ax.text(x, y, z, str(i))
+
+ax.set_axis_off()
+plt.show()
+```
+
+## Best Practices
+
+### Performance
+- For large graphs (>1000 nodes), use simpler layouts (circular, random)
+- Use `alpha` parameter to make dense edges more visible
+- Consider downsampling or showing subgraphs for very large networks
+
+### Aesthetics
+- Use consistent color schemes
+- Scale node sizes meaningfully (e.g., by degree or importance)
+- Keep labels readable (adjust font size and position)
+- Use white space effectively (adjust figure size)
+
+### Reproducibility
+- Always set random seeds for layouts: `nx.spring_layout(G, seed=42)`
+- Save layout positions for consistency across multiple plots
+- Document color/size mappings in legends or captions
+
+### File Formats
+- PNG for raster images (web, presentations)
+- PDF for vector graphics (publications, scalable)
+- SVG for web and interactive applications
+- HTML for interactive visualizations