Related papers: Multiscale network renormalization: scale-invarian…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
We introduce a simple one-parameter network growth algorithm which is able to reproduce a wide variety of realistic network structures but without having to invoke any global information about node degrees such as preferential-attachment…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
The latent space approach to complex networks has revealed fundamental principles and symmetries, enabling geometric methods. However, the conditions under which network topology implies geometricity remain unclear. We provide a…
Scale invariance of an algorithm refers to its ability to treat objects equally independently of their size. For neural networks, scale invariance is typically achieved by data augmentation. However, when presented with a scale far outside…
The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…
The structure of the supply chain network has important implications for modelling economic systems, from growth trajectories to responses to shocks or natural disasters. However, reconstructing firm-to-firm networks from available…
There exist renormalisation schemes that explicitly preserve the scale invariance of a theory at the quantum level. Imposing a scale invariant renormalisation breaks renormalisability and induces new non-trivial operators in the theory. In…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned…
This article addresses the degree distribution of subnetworks, namely the number of links between the nodes in each subnetwork and the remainder of the structure (cond-mat/0408076). The transformation from a subnetwork-partitioned model to…
Random scale-free overlay topologies provide a number of properties like for example high resilience against failures of random nodes, small (average) diameter as well as good expansion and congestion characteristics that make them…
Recently there have been a tremendous interest in models of networks with a power-law distribution of degree -- so called "scale-free networks." It has been observed that such networks, normally, have extremely short path-lengths, scaling…