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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 5: Network Science

SOE 5.3: Vortrag

Dienstag, 10. März 2026, 10:15–10:30, GÖR/0226

Operational time and criticality in physics co-authorship networks — •Pouria Mirelmi¹ and Haiko Lietz² — ¹Leiden University, Leiden, The Netherlands — ²GESIS -- Leibniz Institute for the Social Sciences, Cologne, Germany

Many real-world complex networks display either fractal or small-world structure, but rarely both. Prior work explains this incompatibility through static architectural constraints: fractality emerges from critical branching trees, whereas small-world structure requires supercritical expansion supported by long-range shortcuts. Here we show that this dichotomy is not merely structural but dynamical. Using more than a century of APS co-authorship data, we construct a sequence of network time slices by tuning aggregation to the percolation transition. Measuring a set of macro-level parameters -- including percolation observables and small-world indicators -- we find that all scale as power laws with the networks' distance from criticality. Networks remain fractal near criticality but acquire small-world shortcuts only when aggregated beyond the critical point. We further show that the critical time scale emerging from this aggregation procedure constitutes an operational time to which the system self-organizes: citation avalanches obey dynamical scaling theory only when defined in this intrinsic time. These results indicate that static analyses are insufficient whenever the evolutionary time scale of a network is empirically accessible. A dynamical scaling framework is required to correctly identify and characterize critical and supercritical network states.

Keywords: co-authorship networks; fractality; criticality; operational time; dynamical scaling theory