Module 07: Network Theory for Brain Connectivity

🔗 Circuits as Graphs

Connectomics datasets can be transformed into graphs, where nodes represent neurons and edges represent synapses. This abstraction allows mathematical analysis of the brain's structure using tools from graph theory.

• Graph basics: nodes, edges, adjacency matrices
• Directed vs. undirected graphs
• Weighted edges and multilayer networks

📈 Network Metrics

Network theory provides powerful tools for quantifying connectivity. Key metrics help identify structural features of circuits, such as hubs, communities, and bottlenecks.

• Degree distribution and centrality
• Path length and clustering coefficient
• Network motifs and modularity

🧮 Connectomics in Context

Analyzing neural networks allows us to draw comparisons across species and systems. Biological networks may exhibit small-world or scale-free properties, and can be contrasted with artificial networks.

• Small-world and scale-free architectures
• Comparing biological vs. artificial networks
• Limitations of network abstraction

🎯 COMPASS Integration

• Knowledge: Network terminology and brain graph modeling
• Skills: Data modeling, metric computation, abstraction
• Character: Persistence, openness to complexity
• Meta-Learning: Building bridges between math and biology

📚 References & Resources

• Sporns, 2010. Networks of the Brain. MIT Press.
• Watts & Strogatz, 1998. Collective dynamics of ‘small-world’ networks. Nature.
• NetworkX Documentation: networkx.org
• Notebook: Most Synapses In and Out (source)

✅ Assessment

• Draw a network graph from a small connectome sample
• Compute and interpret degree centrality and clustering coefficient
• Compare two networks (e.g. biological vs. artificial) and describe key differences