Recent biotechnological advances have led to a wealth of biological network data. Topo- logical analysis of these networks (i.e., the analysis of their structure) has led to break- throughs in biology and medicine. The state-of-the-art topological node and network descriptors are based on graphlets, induced connected subgraphs of different shapes (e.g., paths, triangles). However, current graphlet-based methods ignore neighbourhood infor- mation (i.e., what nodes are connected). Therefore, to capture topology and connectivity information simultaneously, I introduce graphlet adjacency, which considers two nodes adjacent based on their frequency of co-occurrence on a given graphlet. I use graphlet adjacency to generalise spectral methods and apply these on molecular networks. I show that, depending on the chosen graphlet, graphlet spectral clustering uncovers clusters en- riched in different biological functions, and graphlet diffusion of gene mutation scores predicts different sets of cancer driver genes. This demonstrates that graphlet adjacency captures topology-function and topology-disease relationships in molecular networks.
To further detail these relationships, I take a pathway-focused approach. To enable this investigation, I introduce graphlet eigencentrality to compute the importance of a gene in a pathway either from the local pathway perspective or from the global network perspective. I show that pathways are best described by the graphlet adjacencies that capture the importance of their functionally critical genes. I also show that cancer driver genes characteristically perform hub roles between pathways.
Given the latter finding, I hypothesise that cancer pathways should be identified by changes in their pathway-pathway relationships. Within this context, I propose pathway- driven non-negative matrix tri-factorisation (PNMTF), which fuses molecular network data and pathway annotations to learn an embedding space that captures the organisation of a network as a composition of subnetworks. In this space, I measure the functional importance of a pathway or gene in the cell and its functional disruption in cancer. I apply this method to predict genes and the pathways involved in four major cancers. By using graphlet-adjacency, I can exploit the tendency of cancer-related genes to perform hub roles to improve the prediction accuracy.