A structure-preserving hybrid-chordal filter for sampling in correlation networksA structure-preserving hybrid-chordal filter for sampling in correlation networks

Biological networks are fast becoming a popular tool for modeling high-throughput data, especially due to the ability of the network model to readily identify structures with biological function. However, many networks are fraught with noise or coincidental edges, resulting in signal corruption. Previous work has found that the implementation of network filters can reduce network noise and size while revealing significant network structures, even enhancing the ability to identify these structures by exaggerating their inherent qualities. In this study, we implement a hybrid network filter that combines features from a spanning tree and near-chordal subgraph identification to show how a filter that incorporates multiple graph theoretic concepts can improve upon network filtering. We use three different clustering methods to highlight the ability of the filter to maintain network clusters, and find evidence that suggests the clusters maintained are of high importance in the original unfiltered network due to high-degree and biological relevance (essentiality). Our filter highlights the advantages of integration of graph theoretic concepts into biological network analysis. Keywords—bioinformatics; clusters; network filters; correlation networks; hub nodes; spanning trees Previous work [5, 6, 7, and 9] reveals that filters imposed on networks generated by correlation of gene expression are an effective means for removing coincidental edges while enhancing biological signal. Duraisamy et al. [9] and Dempsey et al. [5,6] revealed that a filter that removes edges that create large cycles in biological networks (i.e. identifying a chordal subgraph from original graph G) removes about 25% of original edges, maintains clusters that exist in the original network, and also reveals clusters that were previously hidden. Dempsey et al. [7] explored the how a spanning tree filter affects biological relevance of high degree or hub nodes in the correlation network. (Biologically relevant nodes in a correlation network can typically be expected to represent lethal nodes [8, 15], or nodes that represent genes that when knocked out in vivo results in expiration of the organism at some early stage in development [3].) This study found that using a spanning tree filter, it is possible to more accurately identify biologically relevant hub nodes in the correlation network due to the removal of coincidental edges. Further, this enhanced this type of spanning tree filter using a “hybrid” filter that incorporated a spanning tree and a chordal filter by adding edges back into the network. The focus of the study then became the examination of how the biological relevance of hub nodes is further enhanced (i.e., hub nodes from the original network gain more edges back, making them easier to identify as hub nodes). This filter incorporated edge re-addition in two steps, one where edges were added such that chordality is maintained, and a second where edges were added with a less strict condition--chordality is preferred, but not some larger cycles are allowed, if they are part of clusters. The best parameters from this study revealed that adding in edges that did not necessarily maintain chordality (but not adding in all edges) was best able to identify biologically relevant hub nodes. In short, we have four major versions of the network that we are able to test for biological relevance; these variations are shown in Figure 1. “Hub” nodes in correlation networks can be disassortative or assortative [14, 18] (), the former indicating that its neighbors are poorly connected and the latter indicating that the hub is very well connected; in such cases the assortative hub can be found to exist within clusters as a member of a dense community. Results from Dempsey et al. [7] show that while the aforementioned spanning tree (ST) only filter is able