Higher-order Laplacian Renormalization

Information diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, cascading failures in power grids. The critical interactions in networks are the ones that play critical roles in information diffusion and primarily affect network structure and functions. Besides, interactions can occur between not only two nodes as pairwise int...

Higher-order networks are gaining significant scientific attention due to their ability to encode the many-body interactions present in complex systems. However, higher-order networks have the limitation that they only capture many-body interactions of the same type. To address this limitation, we present a mathematical framework that determines the topology of higher-order multiplex networks and illustrates the interplay between their topology and dynamics. Specifically, we ...

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group for complex networks and use the technique to investigate networks as viewed at different scales. We find that real networks embedded in a hidden metric space show geometric scaling, in agreement with the renormalizability of the underlying...

Modern theories of phase transitions and scale-invariance are rooted in path integral formulation and renormalization groups (RG). Despite the applicability of these approaches on simple systems with only pairwise interactions, they are less effective on complex systems with un-decomposable high-order interactions (i.e., interactions among arbitrary sets of units). To precisely characterize the universality of high-order interacting systems, we propose simplex path integral a...

Network science has evolved into an indispensable platform for studying complex systems. But recent research has identified limits of classical networks, where links connect pairs of nodes, to comprehensively describe group interactions. Higher-order networks, where a link can connect more than two nodes, have therefore emerged as a new frontier in network science. Since group interactions are common in social, biological, and technological systems, higher-order networks have...

While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than resorting to handling the bare structure of a network, we overlay it with a readily renormalizable physical model, which reflects real-world scenarios with a broad generality. From the renormalization of the overlying system, we extract a rigorous ...

Nowadays, scaling methods for general large-scale complex networks have been developed. We proposed a new scaling scheme called "two-site scaling". This scheme was applied iteratively to various networks, and we observed how the degree distribution of the network changes by two-site scaling. In particular, networks constructed by the BA algorithm behave differently from the networks observed in the nature. In addition, an iterative scaling scheme can define a new renormalizin...

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw ...

Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate with the different network hierarchies complicating the identification of coexisting mesoscopic structures and functional cores. We present a communicability analysis of effective information p...

Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant research has focused on higher-order networks and ways to represent, analyze, and learn from them. There are two main directions to studying higher-order networks. One direction has focused on capturing higher-order patterns in traditional ...