Related papers: Scaling of internode distances in weighted complex…
We present a new approach to the calculation of measures in weighted networks, based on the translation of a weighted network into an ensemble of edges. This leads to a straightforward generalization of any measure defined on unweighted…
Network analysis has become an increasingly prevalent research tool across a vast range of scientific fields. Here, we focus on the particular issue of comparing network statistics, i.e. graph-level measures of network structural features,…
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link…
The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$.…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
Since some realistic networks are influenced not only by increment behavior but also by tunable clustering mechanism with new nodes to be added to networks, it is interesting to characterize the model for those actual networks. In this…
This article describes a complex network model whose weights are proportional to the difference between uniformly distributed ``fitness'' values assigned to the nodes. It is shown both analytically and experimentally that the strength…
We study the detailed epidemic spreading process in scale-free networks with weight that denote familiarity between two people or computers. The result shows that spreading velocity reaches a peak quickly then decays representing power-law…
This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the…
The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest…
In the field of node representation learning the task of interpreting latent dimensions has become a prominent, well-studied research topic. The contribution of this work focuses on appraising the interpretability of another…
We investigate the role of degree correlation among nodes on the stability of complex networks, by studying spectral properties of randomly weighted matrices constructed from directed Erd\"{o}s-R\'enyi and scale-free random graph models. We…
Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…
We consider nonequilibrium phase transitions in weighted scale-free networks, in which highly connected nodes, which are created earlier in time are partially immunized. For epidemic spreading we solve the dynamical mean-field equations and…
In this paper we deal with the structural properties of weighted networks. Starting from an empirical analysis of a linguistic network, we analyse the differences between the statistical properties of a real and a shuffled network and we…
Complex networks across various fields are often considered to be scale free -- a statistical property usually solely characterized by a power-law distribution of the nodes' degree $k$. However, this characterization is incomplete. In…
In recent years, community structure has emerged as a key component of complex network analysis. As more data has been collected, researchers have begun investigating changing community structure across multiple networks. Several methods…