MIT Press

Table 2.

Graph metric descriptions and interpretations

Graph metric	Description	Higher values mean …	*Previous studies (Adult msTBI^a)*	Related to …
*Integration*
Characteristic path length	The shortest path is the fastest and most direct communication pathway between two network nodes. Characteristic path length is defined as the average shortest path length between all node pairs in a network (Watts & Strogatz, 1998).	A higher characteristic path length indicates that the fastest communication pathways between regions are, on average, longer and less efficient.	Higher characteristic path length (Caeyenberghs et al., 2014; Hellyer et al., 2015; Kim et al., 2014; Pandit et al., 2013; S. Wang et al., 2021).	Verbal learning, executive dysfunction (Kim et al., 2014). Intelligence, working memory span (Königs et al., 2017). Cognitive flexibility and information processing (Hellyer et al., 2015).
Global efficiency	The inverse average shortest path efficiency between all possible pairs of nodes in a network, where efficiency is computed as the inverse of the shortest path length (Latora & Marchiori, 2001).	A higher global efficiency indicates a greater capacity for efficient integration of information (in parallel) across the network.	Lower global efficiency (Caeyenberghs et al., 2014; Kuceyeski et al., 2016; Pandit et al., 2013; S. Wang et al., 2021).	Switching task/attention (Caeyenberghs et al., 2014).
Navigation efficiency	Navigation paths use a decentralized and geometrically greedy heuristic (Boguna et al., 2009). Navigation efficiency is defined as the average navigation path efficiency between all possible pairs of nodes in a network (Seguin et al., 2018).	Higher navigation efficiency indicates greater capacity for efficient integration of information across the network.	Not yet investigated, but lower navigation efficiency observed in stroke patients (X. Wang et al., 2019).
*Segregation*
Clustering coefficient	The number of existing connections between the neighbors of a node, divided by all the possible connections, calculated for each node individually and averaged across the entire network (Watts & Strogatz, 1998).	A higher average clustering coefficient implies that a greater proportion of connections are made between node neighbors, compared with the connections possible, and indicates more clustered connectivity around individual nodes.	Lower clustering coefficient (Hellyer et al., 2015; Raizman et al., 2020).	Cognitive flexibility and information processing (Hellyer et al., 2015).
Normalized clustering coefficient	Clustering coefficient of the network normalized to a random network.	Higher normalized clustering indicates higher local specialization, with a value of 1 being equivalent to a random network. If greater than 1, the network has greater than random clustering. There may be a point of diminishing returns, where greater local specialization comes at the cost of communication efficiency.	Higher normalized clustering^b (Caeyenberghs, Leemans, De Decker, et al., 2012; Verhelst et al., 2018).	Processing speed (van der Horn et al., 2017).
Local efficiency	The local efficiency is the average of inverse shortest path length in a local area. Mean local efficiency is the efficiency of each node in the network averaged over the total number of nodes (Latora & Marchiori, 2001).	A higher local efficiency means greater capacity for integration between the immediate neighbors of a given node.	Higher local efficiency (Jolly et al., 2020); and/or lower local efficiency (Caeyenberghs, Leemans, De Decker, et al., 2012).^b	Reasoning, working memory (Jolly et al., 2020).
*Centrality*
Strength	The strength of a node is the sum of the weights of its edges. Mean strength is the average of all the normalized strength values across each node of the network.	A higher strength indicates a greater average edge weight for each node.	Lower strength (Raizman et al., 2020).
Betweenness centrality	The proportion of shortest paths that pass through node i between its neighboring nodes, calculated for each node and averaged across the network (Freeman, 1978).	Higher betweenness centrality means the node lies on more shortest paths in the network, and thus the node is more central and important to the network. A high network / average betweenness centrality indicates a high number of nodes that are central to shortest paths.	Higher betweenness centrality (Caeyenberghs, Leemans, De Decker, et al., 2012).^b	Associative memory (Fagerholm et al., 2015).

Graph metric	Description	Higher values mean …	*Previous studies (Adult msTBI^a)*	Related to …
*Integration*
Characteristic path length	The shortest path is the fastest and most direct communication pathway between two network nodes. Characteristic path length is defined as the average shortest path length between all node pairs in a network (Watts & Strogatz, 1998).	A higher characteristic path length indicates that the fastest communication pathways between regions are, on average, longer and less efficient.	Higher characteristic path length (Caeyenberghs et al., 2014; Hellyer et al., 2015; Kim et al., 2014; Pandit et al., 2013; S. Wang et al., 2021).	Verbal learning, executive dysfunction (Kim et al., 2014). Intelligence, working memory span (Königs et al., 2017). Cognitive flexibility and information processing (Hellyer et al., 2015).
Global efficiency	The inverse average shortest path efficiency between all possible pairs of nodes in a network, where efficiency is computed as the inverse of the shortest path length (Latora & Marchiori, 2001).	A higher global efficiency indicates a greater capacity for efficient integration of information (in parallel) across the network.	Lower global efficiency (Caeyenberghs et al., 2014; Kuceyeski et al., 2016; Pandit et al., 2013; S. Wang et al., 2021).	Switching task/attention (Caeyenberghs et al., 2014).
Navigation efficiency	Navigation paths use a decentralized and geometrically greedy heuristic (Boguna et al., 2009). Navigation efficiency is defined as the average navigation path efficiency between all possible pairs of nodes in a network (Seguin et al., 2018).	Higher navigation efficiency indicates greater capacity for efficient integration of information across the network.	Not yet investigated, but lower navigation efficiency observed in stroke patients (X. Wang et al., 2019).
*Segregation*
Clustering coefficient	The number of existing connections between the neighbors of a node, divided by all the possible connections, calculated for each node individually and averaged across the entire network (Watts & Strogatz, 1998).	A higher average clustering coefficient implies that a greater proportion of connections are made between node neighbors, compared with the connections possible, and indicates more clustered connectivity around individual nodes.	Lower clustering coefficient (Hellyer et al., 2015; Raizman et al., 2020).	Cognitive flexibility and information processing (Hellyer et al., 2015).
Normalized clustering coefficient	Clustering coefficient of the network normalized to a random network.	Higher normalized clustering indicates higher local specialization, with a value of 1 being equivalent to a random network. If greater than 1, the network has greater than random clustering. There may be a point of diminishing returns, where greater local specialization comes at the cost of communication efficiency.	Higher normalized clustering^b (Caeyenberghs, Leemans, De Decker, et al., 2012; Verhelst et al., 2018).	Processing speed (van der Horn et al., 2017).
Local efficiency	The local efficiency is the average of inverse shortest path length in a local area. Mean local efficiency is the efficiency of each node in the network averaged over the total number of nodes (Latora & Marchiori, 2001).	A higher local efficiency means greater capacity for integration between the immediate neighbors of a given node.	Higher local efficiency (Jolly et al., 2020); and/or lower local efficiency (Caeyenberghs, Leemans, De Decker, et al., 2012).^b	Reasoning, working memory (Jolly et al., 2020).
*Centrality*
Strength	The strength of a node is the sum of the weights of its edges. Mean strength is the average of all the normalized strength values across each node of the network.	A higher strength indicates a greater average edge weight for each node.	Lower strength (Raizman et al., 2020).
Betweenness centrality	The proportion of shortest paths that pass through node i between its neighboring nodes, calculated for each node and averaged across the network (Freeman, 1978).	Higher betweenness centrality means the node lies on more shortest paths in the network, and thus the node is more central and important to the network. A high network / average betweenness centrality indicates a high number of nodes that are central to shortest paths.	Higher betweenness centrality (Caeyenberghs, Leemans, De Decker, et al., 2012).^b	Associative memory (Fagerholm et al., 2015).

^a

msTBI: Moderate to severe traumatic brain injury.

^b

This study is of young adults and children with TBI.