Alzheimer’s disease (AD) is characterized by complex alterations in brain connectivity, making the understanding of these patterns critical for early diagnosis and intervention. This study presents a motif-based analysis of functional brain connectivity utilizing synthetic adjacency matrices of virtual connectomics derived from Alzheimer’s Disease Neuroimaging Initiative (ADNI) data. Our approach involves first sparsifying the functional brain network to enhance the significance of the connections, followed by the construction of a directed network from bidirectional correlation-based edge weights between ROIs (Regions of Interest) to accurately capture the flow of information. By systematically searching for recurrent motifs within these networks, we aim to identify specific patterns of connectivity that may distinguish AD patients from healthy controls. Motifs are fundamental building blocks that provide insights into the functional organization of the brain and can reveal underlying mechanisms of neurodegeneration. This analysis not only contributes to the characterization of brain network alterations in AD but also demonstrates the utility of synthetic connectomes in neuroimaging research. Our findings have implications for developing network-based biomarkers and enhancing our understanding of the pathophysiology of Alzheimer’s disease, highlighting the importance of integrating advanced network analysis techniques to unravel the complexities of brain connectivity in neurodegenerative conditions.

In this paper, we focus on network robustness in complex networks by identifying those links within a network graph G whose attack/removal would cause a severe network damage. More specifically, we investigate the role of the effective resistance matrix in identifying an order of links more vulnerable to attacks. In our previous works, we have both evaluated a strategy of link removals based on the ranking provided by the Hadamard product matrix between the adjacency matrix of G and the effective resistance matrix, and a strategy of node removals based on the ranking of the diagonal elements of the pseudoinverse of the Laplacian matrix associated to G. Now, through a real-world networking scenario of an Internet backbone, we start considering the line graph L(G) of G (i.e. the dual graph in which the links of G are nodes). Then, we investigate if removing nodes in the line graph is the same as removing links in G. The relation between the Laplacian of the line graph and the graph itself is not obvious, which does not allow us to immediately map the performance of a node removal strategy to the performance of a link removal strategy. Carrying out our analysis on Erdős-Rényi, Watts-Strogatz and Bárabasi-Albert networks, we look for a relation, if existing, between (a) the node removal in the line graph of G and (b) the link removal in G. Results show that the two attack strategies show a notable degree of similarity mostly on the Bárabasi-Albert networks.