Emergence in networks explained by paths crossing boundaries
Emergence in Network Systems is Bounded by Boundary-Crossing Paths
Social and Information Networks
Summary
Emergence means that a whole system shows features that individual parts don’t have alone. The authors show that these new features come from paths crossing boundaries between parts in a network. They prove that the amount of emergence can be measured by counting such boundary-crossing paths. Their method works locally, lets you see which parts cause emergence, and can guide designing systems with desired features.
What this means in practice
- •For network engineers: Identify key routes causing emergent behaviors to improve network design and reliability.
- •For neuroscience modelers: Trace how specific neuron pathways contribute to overall brain function emergence for better simulation models.
Authors
Johnny Jingze Li, Gabriel A. Silva
Abstract
Emergence, features of a whole that no part shows alone, is central to complex systems but rarely measured so as to locate its source. Viewing a system structurally, as a network of interacting parts, we evaluate emergence as what observing the coupled whole reveals beyond, or erases from, the combined observations of the parts. For observations that build what they see route by route, we show that every emergent feature is produced by its own route across the interface between parts, a route that traces it to the components and interactions responsible. We show the number of all such boundary-crossing paths bounds the total emergence discrepancy, and equals the emergence of measures that count routes. The bound is computed locally around the interface, validated through network examples, and in a nervous system the routes show that interneurons relay most of the emergence. Our work associates emergence with path structure in the network system that can be anticipated, attributed, and engineered.