In graph theoretical modeling, a network is composed of a certain number of nodes that are connected by weighted or un-weighted edges. A graph can be classified as a director or undirected type, depending on the existence or absence of directional information associated with the edges. In human brain development studies, the macro-scale network is often used. It is a model that can record the inter-regional connections in the whole brain in vivo through neuroimaging data. Network modes in this model are usually defined by brain partitions that are previously assigned, and the edges are determined by the structural or functional interactions between the separate brain regions.

What is the graph theoretical modeling framework?

In graph theoretical modeling, a network is composed of a certain number of nodes that are connected by weighted or un-weighted edges. A graph can be classified as a director or undirected type, depending on the existence or absence of directional information associated with the edges. In human brain development studies, the macro-scale network is often used. It is a model that can record the inter-regional connections in the whole brain in vivo through neuroimaging data. Network modes in this model are usually defined by brain partitions that are previously assigned, and the edges are determined by the structural or functional interactions between the separate brain regions.

How are network nodes defined?

Acquiring network nodes relies on neuroimaging. In EEG, fNIRS, and MEG studies, nodes are determined by using their derived cortical locations of electrodes, detectors, or sensors. In MRI studies, a parcellation scheme or atlas is needed to divide the brain into different regions of interest which are defined based on anatomical or functional information or on a random algorithm. Different parcellations capture different patterns of structural or functional pathways. The number of nodes significantly influences the absolute value of topological attributes.

How are network edges defined?

Brain regions are structurally connected through a large number of fiber bundles that provide biological pathways for information transfer. Through dMRI-based tractography, these fiber tracts can be reconstructed and then used to define edges of the structural connectivity network. The number of reconstructed streamlines or averaged informative diffusion indexes of the connection can be used as the edge weight.

What is network thresholding?

Before obtaining the brain network, a thresholding step is usually performed to define the edges to be used in the subsequent graph theoretical analysis, though some studies use the raw weighted network without thresholding. There are different ways of doing this:

• Setting an absolute cut-off value to select edges with greater weights in an individual network. Excluding weak edges may reduce the effects of weak covariance or spurious connections that could be caused by imaging noise, cumulative tractography errors, or head motions.
• In proportional thresholding a fixed number of the strongest connections are retained in each subject. It equals the network density across individuals to minimize its influence on network topological properties, though it may ignore potentially valuable connections.

What are global and nodal aspects?

The topology of a brain network can be characterized in terms of its global and nodal aspects. The global attributes measure the architecture of the whole network graph. The nodal attributes measure topological features of a single node.

What is meant with the segregation of a network?

The segregation of a network refers to the ability of local information processing that is responsible for specialized functions. The clustering coefficient and modularity are two attributes that provide a quantitative measurement of the segregation capacity of brain network.

What is the clustering coefficient of a node and of a network?

The clustering coefficient of a node refers to the tendency to which the neighboring nodes of a node are interconnected. It reflects the density of local clusters. The clustering coefficient of a network refers to the average nodal clustering coefficients across all nodes in the network.

What is meant with the integration of a network?

Network integration refers to the ability of parallel communication with distributed nodes which can be quantitatively measured by the characteristic path length or global efficiency. The characteristic path length of a network can be calculated by averaging the shortest path lengths between each pair of nodes in the network. A path represents a route of edges that connect one node with others. Its length is defined as the sum of the number or weights of the edges. The global efficiency of a network is the inverse of the average values of the shortest path length between any two nodes. A high degree of network integration is seen in a network that has high global efficiency and the low shortest path length has high global information transfer efficiency.

What is a small-world network?

A small-world network possesses a shorter characteristic path length than a regular network and a higher clustering coefficient than a random network, to guarantee high capacity for local and global information transfer networks. It is an optimized topology that balanced between a regular and a random network. A regular network has a high clustering coefficient and long characteristic path length. A random network has a low clustering coefficient and a short characteristic path length.

What is nodal degree?

Nodal degree is the most direct nodal metric, referring to the number of edges linking to a node. High degree nodes function as hubs in information transmission. The degree distribution of a network indicated the proportion of nodes that have a certain degree, which can be an indication of the resilience of the network. Rich-club organization refers to highly connected hubs, indicating that the hub nodes tend to be more densely interconnected with each other than by random chance would be expected.

Which types of network edges are distinguished?

The network edges can be classified into three types:

• Rich-club connections which link between rich-club nodes.
• Feeder connections which link between peripheral and core nodes.
• Local connections which link between non-rich-club nodes.

How does the prenatal brain network develop?

The prenatal structural network already shows broadly adult-like topological structures. The network is already highly efficient at local and global information transfers, possessing the specialized local communities for segregation and the high-cost backbones for integration. Increased normalized clustering coefficient, stable normalized shortest path length, and increasing small-worldness with development indicate that the shaping of the network seems to lean toward segregation enforcement during the prenatal stage. Short-range connections develop fast, hub regions expand into the inferior frontal cortex and insula regions and develop fast on their nodal connectivity and nodal betweenness centrality.

How does the postnatal brain network develop?

Structural segregation appears to be decreasing while structural integration is increasing, as can be seen by decreased modularity and characteristic path length and increased number of inter-module connectors and global efficiency. During early postnatal life there is dynamic regional reshaping in the structural network, as expressed by upgrades in network robustness and the left anterior cingulate gyrus and left superior occipital gyrus which become hubs. Neonatal functional brain networks maintain highly efficient small-world and modularity structure. The dorsal attention network and default mode network mature at one year of life, whereas the salience network and bilateral frontoparietal network are still developing at that time.

What is the topological development of the baby brain network?

With regards to the structural network, the hypothesis is that the structural network is well-established at the time of birth, with many local connections within modules and several major distant connections between modules. With development, the network becomes more segregated with enhancement of local clusters during prenatal development. Then it becomes more integrated with increasing inter-module connections during postnatal development. With regards to the functional network, the hypothesis is that it is still immature and incomplete at birth. With development, the network shows enhanced segregation during prenatal development. Then the emergence and increase of long connections intensify the integrated ability of networks.

How does preterm growth affect the development of the brain network?

Preterm growth is the most common type of early atypical growth. It involves the sudden interruption of typical development processes as a result of complex genetic and environmental processes. The abnormal brain topology is characterized by disruptions in cortical-subcortical connectivity and short-distance cortico-cortical connections, as well as reduced edge strengths in widespread tracts, increased clustering coefficient, and increased nodal clustering coefficients located at the lateral parietal, ventral, and lateral frontal cortices. The changes in brain network caused by preterm birth continue into later life.