Understanding neuronal connectivity has become a
central focus of neuroscience in light of several unprecedented, large-scale
international initiatives to comprehensively map wiring diagrams of nervous
systems – so-called connectomes – at resolutions ranging from the microscopic
(on the scale of a few nanometers) to macroscopic (on the scale of millimeters
and centimeters). The diversity of the data produced by these efforts, which is
collected using measurement techniques that include electron microscopy, tract
tracing and magnetic resonance imaging, and in species such as the nematode
worm, Drosophila fruit fly, mouse, macaque and human, pose a major challenge
for systematic evaluation, comparison and integration across studies.

Graph theory – a branch of mathematics concerned with modeling systems of interacting elements – provides a unifying and powerful framework for characterizing these varied data. It rests on the assumption that any network can be represented in abstract form as a graph of nodes connected by edges. In connectomics, the nodes correspond to neurons or neuronal populations and the edges to structural or functional connections.

Graph theory has had a major impact on neuroscience, revealing new insights into the organizational properties of brain networks and their generative mechanisms. Many such properties are conserved across resolution scales, measurement technique and species, suggesting that they are fundamental aspects of neural structure and function. Graph theory has also provided a powerful platform for mapping, at a connectome-wide level, the effects of disease and other experimental manipulations.

This workshop provides an integrated overview of the field, covering both basic concepts and advanced applications in the graph theoretic analysis of brain networks. The first half of the workshop will focus on fundamentals such as how a network graph is constructed from neural connectivity data; the different types of graph models available for brain networks; key graph theoretic concepts and measures such as small-worlds, clustering, paths, diffusion processes, centrality, hubs, and modularity; statistical methods for connectome-wide analyses; and the clinical applications of graph theory. The second half of the workshop will consider advanced topics, including the integration of graph theoretic models across resolution scales and other kinds of ‘omics data; the use of multilayer networks in modeling dynamic changes in brain connectivity and other applications; generative modeling of brain network organization; the analysis of high-resolution functional connectivity networks with magnetoencephalography; and the way in which graph theory can be used to understand how disease spreads through brain networks.

Graph theory will play an increasingly important role in attempts to understand the massive amounts of data generated by large collaborative projects such as the Human Connectome Project. An integrated and comprehensive educational workshop on the topic is thus timely and necessary to provide researchers with the knowledge required to make the most of such rich data. Attendees will leave this workshop with a detailed understanding of the fundamental principles of graph theory, the application of graph theoretic methods to neuroscientific data, and insight into emerging trends and advanced applications. Attendees will also understand the correct use and interpretation of core graph theoretic measures and the limitations of graph theoretic models.

Graph theory – a branch of mathematics concerned with modeling systems of interacting elements – provides a unifying and powerful framework for characterizing these varied data. It rests on the assumption that any network can be represented in abstract form as a graph of nodes connected by edges. In connectomics, the nodes correspond to neurons or neuronal populations and the edges to structural or functional connections.

Graph theory has had a major impact on neuroscience, revealing new insights into the organizational properties of brain networks and their generative mechanisms. Many such properties are conserved across resolution scales, measurement technique and species, suggesting that they are fundamental aspects of neural structure and function. Graph theory has also provided a powerful platform for mapping, at a connectome-wide level, the effects of disease and other experimental manipulations.

This workshop provides an integrated overview of the field, covering both basic concepts and advanced applications in the graph theoretic analysis of brain networks. The first half of the workshop will focus on fundamentals such as how a network graph is constructed from neural connectivity data; the different types of graph models available for brain networks; key graph theoretic concepts and measures such as small-worlds, clustering, paths, diffusion processes, centrality, hubs, and modularity; statistical methods for connectome-wide analyses; and the clinical applications of graph theory. The second half of the workshop will consider advanced topics, including the integration of graph theoretic models across resolution scales and other kinds of ‘omics data; the use of multilayer networks in modeling dynamic changes in brain connectivity and other applications; generative modeling of brain network organization; the analysis of high-resolution functional connectivity networks with magnetoencephalography; and the way in which graph theory can be used to understand how disease spreads through brain networks.

Graph theory will play an increasingly important role in attempts to understand the massive amounts of data generated by large collaborative projects such as the Human Connectome Project. An integrated and comprehensive educational workshop on the topic is thus timely and necessary to provide researchers with the knowledge required to make the most of such rich data. Attendees will leave this workshop with a detailed understanding of the fundamental principles of graph theory, the application of graph theoretic methods to neuroscientific data, and insight into emerging trends and advanced applications. Attendees will also understand the correct use and interpretation of core graph theoretic measures and the limitations of graph theoretic models.