Laplacian Renormalization Group for heterogeneous networks


Thursday, January 18, 2024
11:00 - 12:30


Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales, reflecting structural insights not manifested from network topology analyses. Moreover, small-world effects correlate with network hierarchies, complicating identifying coexisting mesoscopic structures and functional cores. To shed further light on these issues, we present a communicability analysis of effective information pathways throughout complex networks based on information diffusion. This leads us to formulate a new renormalization group scheme for heterogeneous networks. The Renormalization Group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is particularly challenging due to correlations between intertwined scales. The Laplacian RG picture for complex networks defines the supernodes concept à la Kadanoff and the equivalent momentum space procedure à la Wilson for graphs. A direct application of the Laplacian Renormalization Group (LRG) framework is the multi-scale Laplacian (MSL) community detection algorithm. Based on inter-node communicability, our definition provides a unifying framework for multiple partitioning measures.


Dutch Institute for Emergent Phenomena (DIEP)


Institute for Advanced Study

Room number

2nd floor library




complexity, computational physics, condensed matter theory, emergence, soft matter


Tommaso Gili

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