Abstract
We know that functional and structural organization is altered in human brain network due to Alzheimer’s disease. In this paper we highlight how Graph Theory techniques, its structural parameters like connectivity, diameter, vertex centrality, betweenness centrality, clustering coefficient, degree distribution, cluster analysis and graph cores are involved to analyse magnetoencephalography data to explore functional network integrity in Alzheimer’s disease affected patients. We also record that both weighted and unweighted undirected/directed graphs depending on functional connectivity analysis with attention to connectivity of the network and vertex centrality, could model and provide explanation to loss of links, status of the hub in the region of parietal, derailed synchronization in network and centrality loss at the vital left temporal region that is clinically significant were found in cases carrying Alzheimer’s disease. We also notice that graph theory driven measures such as characteristic path length and clustering coefficient could be used to study and report a sudden electroencephalography effect in Alzheimer’s disease through entropy of the cross-sample. We also provide adequate literature survey to demonstrate the latest and advanced graphical tools for both graph layouts and graph visualization to understand the complex brain networks and to unravel the mysteries of Alzheimer’s disease.
Highlights
Networks are deemed as a collection of certain objects and links joining them
Euler proved beyond doubt this fact with a crisp two-page argument. This has led to the birth of a branch of mathematics called, Graph Theory
We call a vertex ur is a neighbour of vertex us, if e(r, s) ∈ E, and the number of neighbours ur has is refereed as degree centrality (DC) of that vertex. the DC of vertex ur in an undirected graph is DC(ur ) = Σur,s = Σus,r where s = 1 to n and for a digraph we introduce DCin and DCout referred respectively as the in-degree/out-degree and write DCin = Σusr where s = 1 to n and DCout = Σurs where s = 1 to n
Summary
Networks are deemed as a collection of certain objects and links joining them. K. Narayanaa define networks and characterizes its properties. The word Graph was coined from the Greek term Graphos that stands for something that is drawn
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