Short and Wide Network Paths

TL;DR

This paper introduces a new model of network flow emphasizing short and wide paths, develops algorithms to find such paths, and applies this to biological networks to understand information processing constraints.

Contribution

It proposes a pipelined network flow model with algorithms for identifying optimal paths, and applies this to biological networks to reveal organizational principles.

Findings

Short and wide paths optimize flow in networks.

Biological networks exhibit these paths and constraints.

Functional subcircuits are key organizational units.

Abstract

Network flow is a powerful mathematical framework to systematically explore the relationship between structure and function in biological, social, and technological networks. We introduce a new pipelining model of flow through networks where commodities must be transported over single paths rather than split over several paths and recombined. We show this notion of pipelined network flow is optimized using network paths that are both short and wide, and develop efficient algorithms to compute such paths for given pairs of nodes and for all-pairs. Short and wide paths are characterized for many real-world networks. To further demonstrate the utility of this network characterization, we develop novel information-theoretic lower bounds on computation speed in nervous systems due to limitations from anatomical connectivity and physical noise. For the nematode Caenorhabditis elegans, we find these bounds are predictive of biological timescales of behavior. Further, we find the particular C. elegans connectome is globally less efficient for information flow than random networks, but the hub-and-spoke architecture of functional subcircuits is optimal under constraint on number of synapses. This suggests functional subcircuits are a primary organizational principle of this small invertebrate nervous system.