Networks Generate Mass Using Particle Physics

A mechanism to generate massive excitations within graph structures mirrors concepts from particle physics, as shown by Ioannis Kleftogiannis and Ilias Amanatidis of the National Center for Theoretical Sciences. They treat a graph’s connectivity, specifically the number of connections each point possesses, as a fundamental field. Inspired by the Higgs mechanism in quantum field theory, they coupled this ‘degree field’ to a field derived from the graph’s edges, resulting in emergent massive particles propagating within the network. The study reveals that the mass of these particles correlates with the density of the graph, with heavier particles concentrating in highly connected regions and lighter particles spreading across fewer points, suggesting that matter-like structures can arise from simple connectivity rules.

Network topology induces emergent mass scales via a Higgs-like mechanism

The incident matrix served as a table listing connections within the network, enabling the introduction of directionality to the graph’s edges and modelling them as a vector-like field. Treating the number of connections each point has as a fundamental property of the graph created a ‘degree field’. This coupling, inspired by the Higgs mechanism, generated massless and massive excitations, effectively creating ‘particles’ within the network’s structure. Consequently, an emergence of a ‘mass gap’ occurred, representing the difference in ‘weight’ between these particles.

Investigations of graph structures consisting of n vertices and m edges were undertaken, randomly connected to model complex networks. The density of these graphs, represented by the ratio R of edges to vertices (m/ n), influenced the resulting ‘mass gap’ and the behaviour of ‘massive excitations’ within the network. This approach explored emergence without assuming pre-existing spacetime or particle definitions, unlike alternatives that typically rely on established physics principles. A certain density impacted the mass gap, peaking before declining as graphs approached complete connectivity; the average mass gap initially increased with density, reaching a maximum before decreasing as the graph became fully connected, a behaviour observed across varying graph sizes, including those with n vertices.

Mass generation correlates with network topology and density

Now, the most massive excitations localize on just a few vertices, a marked improvement over prior methods which required excitations to spread across many. This threshold represents a fundamental shift; previously, generating mass within graph-based models necessitated complex assumptions about connectivity and spacetime, but now it arises from simple network properties. An institution’s scientists have demonstrated that the emergence of matter-like structures with varying mass properties is possible in discrete physical models, relying solely on graph connectivity.

Excitations with intermediate masses spread across more vertices, while the lightest excitations concentrate on those with smaller degrees, revealing a clear relationship between mass and network position. The analysis of the incidence matrix revealed that heavier, more massive excitations concentrated on areas of high graph density, specifically vertices with a large degree, while lighter excitations spread across fewer vertices with smaller degrees. Although these discrete models successfully generate matter-like structures and establish a link between network properties and mass, they do not yet demonstrate how to scale these findings to represent complex physical systems or predict real-world particle behaviour.

Emergent mass demonstrated within network structures without additional fields

Understanding how complex systems generate emergent properties has long been a goal for scientists, and this work offers a compelling new angle by demonstrating how ‘mass’ can arise within the simple framework of network connections. The current study deliberately confines itself to proving the possibility of this mechanism, leaving unanswered the vital question of where, or even if, such emergent mass properties manifest in tangible physical systems. Nevertheless, even acknowledging that this research presently demonstrates only the potential for mass to emerge from network structure, its value remains considerable.

This work provides a new, minimalist framework for thinking about how fundamental properties like connectivity could give rise to more complex phenomena, sidestepping the need for pre-existing fields or assumptions about extra dimensions. A mechanism for generating mass within graphs has been established, treating network connectivity as a fundamental property akin to a field in particle physics. Researchers created ‘massive excitations’ behaving like emergent particles by modelling the number of connections at each point as a ‘degree field’ and coupling it to a field derived from the graph’s edges. In particular, the heaviest of these excitations concentrate in densely connected areas of the graph, while lighter ones spread more widely, demonstrating a relationship between mass and network location.

The research demonstrated a mechanism for generating massive excitations within graph structures, effectively creating emergent particles. This finding suggests that mass-like properties can arise from the connectivity of a network, without requiring additional fields or dimensions. The mass of these excitations correlated with network density, with heavier particles localising in highly connected regions and lighter particles spreading more widely. Researchers modelled these effects using graphs and their associated incident matrices, exploring how graph size and density influence the resulting mass gap and particle localisation.