Complex Brain Networks: A Graph-Theoretical Analysis

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of individuals. The authors used 997 samples from the Human Connectome

Project and concluded that the swap distance is directly proportional to the

familial distances and ages of the subjects. They also found that this distance

is lower in females compared to males and is greater for females with lower

cognitive scores compared to females with larger cognitive scores. Regions

that affected swap distances significantly were in higher-order networks which

are default-mode and fronto-parietal which perform executive function and

memory.

Choosing an atlas for parcellation of the brain to yield connectome is a

crucial task in the graph-theoretical analysis of the brain. The robustness of

a built atlas in constructing network topology may be determined by find-

ing the similarity across a number of connectomes. Graph matching to assess

the similarity of connectomes built from atlases is used in [24] by introducing

the graph Jaccard index (GJI) based on the Jaccard index. The authors also

propose WL-align method derived from the Weisfeiler-Leman (WL) graph-

isomorphism test to align connectomes. Subjects from the Human Connec-

tome Project database are used to validate the proposed GJI and WL-align

method and a strategy is proposed to choose a suitable parcellation scheme

for structural connectivity. Brain parcellation may be performed in network

domain using a suitable network alignment algorithm, without using an atlas

as described in [25]. The authors implement and compare six global network

alignment algorithms in brain networks: MAGNA [26], NETAL [27], GHOST

[22], GEDEVO [28], WAVE [29], and Natalie2.0 [30]. They conclude that the

best results in terms of edge conservation were obtained when MAGNA++

which is an extension to MAGNA as global aligner was used. MAGNA is a

global network aligner based on a genetic algorithm that uses the evolution

of a population of alignments over time.

An unsupervised graph matching method is used in [31] to align structural

connectomes of a set of healthy subjects with parcellations of varying granular-

ities. Four different algorithms are used for initialization: Spatial Adjacency,

Identity, Barycenter, and Random. The resulting permutations indicate that

applying the alignment methods improve the similarity of subjects when the

number of parcels is greater than 100 and when Spatial Adjacency and Identity

initializations are used. The authors also state that permutations are observed

mostly among neighbor parcels and that the spatial distribution of the permu-

tations indicate all the regions across the context are mostly permuted with

first and second-order neighbors.

9.7

Disease Networks of the Brain

Diagnosis of a brain disease traditionally is commonly performed by self-

reported symptoms and clinical signs of the patient. Investigation of the brain

networks for the diagnose of neurological diseases such as Alzheimer’s disease