Centrality and Hubs

This lecture covers the concepts of centrality and hubs in network neuroscience, exploring the three cardinal axes of centrality: degree, betweenness, and closeness. It delves into the importance of eigenvectors, clustering coefficients, small-world networks, and network failures. The instructor discusses the significance of hubs in the brain's structural connectome, the connectedness of networks, and the emergence of the giant component in random graphs. Percolation theory and its application in brain networks are also addressed, highlighting the movement and filtering of fluids through porous materials.

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EE-619: Advanced topics in network neuroscience

The main goal of this course is to give the student a solid introduction into approaches, methods, and tools for brain network analysis. The student will learn about principles of network science and

Centrality

In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.

Small-world experiment

The small-world experiment comprised several experiments conducted by Stanley Milgram and other researchers examining the average path length for social networks of people in the United States. The research was groundbreaking in that it suggested that human society is a small-world-type network characterized by short path-lengths. The experiments are often associated with the phrase "six degrees of separation", although Milgram did not use this term himself.

Connectome

A connectome (kəˈnɛktoʊm) is a comprehensive map of neural connections in the brain, and may be thought of as its "wiring diagram". An organism's nervous system is made up of neurons which communicate through synapses. A connectome is constructed by tracing the neuron in a nervous system and mapping where neurons are connected through synapses. The significance of the connectome stems from the realization that the structure and function of the human brain are intricately linked, through multiple levels and modes of brain connectivity.

Random graph

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs.

Betweenness centrality

In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph, there exists at least one shortest path between the vertices such that either the number of edges that the path passes through (for unweighted graphs) or the sum of the weights of the edges (for weighted graphs) is minimized. The betweenness centrality for each vertex is the number of these shortest paths that pass through the vertex.

Centrality and Hubs EE-619: Advanced topics in network neuroscience

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Graph Statistics: Random Graphs, Graph Homomorphisms, and Network Analysis MATH-448: Statistical analysis of network data

Explores graph statistics, random graph generation, network analysis, centrality measures, and clustering coefficients.