Related papers: Fractal Boundaries of Complex Networks
We present a detailed analytical and numerical study for the spreading of infections in complex population networks with acquired immunity. We show that the large connectivity fluctuations usually found in these networks strengthen…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
Human social behavior is organized in stratified, hierarchical networks, with a support group with about 5 members, expanding proportionally at each layer up to a maximum of approximately 150 frequent interactions per individual. This is…
In the paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing susceptibilities of different networks to changes in external fields. In the…
Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average…
Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…
In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…
We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks…
This paper studies the effect of boundary value conditions on consensus networks. Consider a network where some nodes keep their estimates constant while other nodes average their estimates with that of their neighbors. We analyze such…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
Networks composed from both connectivity and dependency links were found to be more vulnerable compared to classical networks with only connectivity links. Their percolation transition is usually of a first order compared to the second…
Fractal (or transfractal) features are common in real-life networks and are known to influence the dynamic processes taking place in the network itself. Here we consider a class of scale-free deterministic networks, called $(u,v)$-flowers,…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
In this paper we consider the dyadic effect introduced in complex networks when nodes are distinguished by a binary characteristic. Under these circumstances two independent parameters, namely dyadicity and heterophilicity, are able to…
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…