Abstract
We introduce basic concepts of brain networks and discuss methods to model and analyze brain molecular connectivity using positron emission tomography (PET) and single-photon emission computed tomography (SPECT). Basic elements of network analytic methods, including graph theory, and the connectivity matrix as a basis for network analysis will be discussed in more detail. Statistical methods to compare networks will be reviewed. A specific brain network analysis method called sparse inverse covariance estimation (SICE) is presented as an alternative to Pearson correlation to estimate the brain molecular connectivity matrix. Finally, we will discuss examples from published research to illustrate the practical application of brain molecular connectivity analysis concepts.
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A Lexicon of the Most Commonly Used Network Metrics
A Lexicon of the Most Commonly Used Network Metrics
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Shortest path: Topological distance between two nodes, also called Length, as the minimum number of edges between two nodes.
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Path length: Shortest path of a given node to each of the other nodes.
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Characteristic path length: Average path length node across all nodes.
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Global efficiency: Average of the inverse shortest path from a given node to all other nodes. At the network level, it is the average of the global efficiency of all nodes.
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Triad: Formed when a node is connected to any two connected neighbors.
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Clustering coefficient: The ratio between the number of triads present around a node and the maximum number of triads that could be formed around that node. At the network level, it is the average of the clustering coefficient of all nodes.
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Local efficiency (nodal level): The global efficiency calculated on the subgraph created by the node’s neighbors. At the network level, it is the average of the local efficiency of all nodes.
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Modularity: The extent to which a network can be subdivided into modules (communities of nodes) with a maximal within-module and minimal between-module connectivity.
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The small-worldness (σ): The extent to which a network shows an optimal balance between characteristic path length (integration) and average clustering coefficient (segregation).
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Degree: The number of direct connections that a node has with other nodes. At the network level, it is the average of the degrees of all nodes.
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Strength: The sum of the weights of all edges connected to a node. At the network level, it is the average of the strength of all nodes.
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Closeness centrality: The same as the global efficiency at the nodal level.
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Betweenness centrality: The ratio between all shortest paths that pass through the node and all shortest paths in the graph.
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Participation coefficient: The ratio between the number of connections that the node has outside its module (intermodular) and the total number of connections in the whole network.
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Within-module degree z-score: The nodal degree but restricted to only connections inside the module to which that node belongs.
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Sanchez-Catasus, C.A., Müller, M.L.T.M., De Deyn, P.P., Dierckx, R.A.J.O., Bohnen, N.I., Melie-Garcia, L. (2021). Use of Nuclear Medicine Molecular Neuroimaging to Model Brain Molecular Connectivity. In: Dierckx, R.A.J.O., Otte, A., de Vries, E.F.J., van Waarde, A., Leenders, K.L. (eds) PET and SPECT in Neurology. Springer, Cham. https://doi.org/10.1007/978-3-030-53168-3_8
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