Contact networks have small metric backbones that maintain community structure and are primary transmission subgraphs

Abstract

The structure of social networks strongly affects how different phenomena spread in human society, from the transmission of information to the propagation of contagious diseases. It is well-known that heterogeneous connectivity strongly favors spread, but a precise characterization of the redundancy present in social networks and its effect on the robustness of transmission is still lacking. This gap is addressed by the recently introduced metric backbone, a subgraph that is sufficient to compute all shortest paths of weighted graphs. We show that the metric backbones of nine contact networks obtained from proximity sensors in a variety of social contexts are generally very small, 49% of the original graph for one and ranging from about 6% to 20% for the others. This reflects a surprising amount of redundancy and reveals that shortest paths on these networks are very robust to random attacks and failures. We show that the metric backbone preserves the community structures of the full contact networks and is a primary subgraph in epidemic transmission. The metric backbone, thus, is a principled graph reduction technique that does not affect shortest path connectivity for any nodes in a network. It is an important subgraph to characterize epidemic spread, the robustness of social networks, and any communication dynamics that depend on complex network shortest paths.

The conserved genetic program of male germ cells uncovers ancient regulators of human spermatogenesis

“…The metric backbone is the subgraph that is sufficient to compute all shortest paths in the network, thus removing edges that break the triangle inequality (and are therefore redundant in regards to the shortest paths). This network retains all metric edges and preserves all the nodes in the original network 12,13 . Considering that a set of the PPI in each layer are evolutionarily-conserved, we developed the orthoBackbone: a single shared subnetwork obtained by collapsing the metric backbone of all layers according to the orthologous relationships.…”

“…We have previously shown that it is possible to simplify the complexity of biological networks by removing network redundancy as to only retain the key edges that sustain the system 24 . These edges form the network backbone and are calculated based on the minimum number of shortest paths (proxy to the most relevant interactions) required to maintain network integrity 25 . In the context of transcriptome networks, the backbone uncovers the essential gene interactions that define core pathways in the gene expression program 26 .…”

Regulatory changes associated with the head to trunk developmental transition

“…The metric backbone is a subgraph that is sufficient to compute all shortest paths in the network, thus removing edges that break the triangle inequally (and are therefore redundant regarding the shortest paths). This network retains all metric edges and preserves all the nodes in the original network [36, 115]. We have previously used the metric backbone of transcriptome networks to identify biologically relevant genes and their interactions [37].…”