Related papers: Properties of weighted complex networks
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The…
We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be…
This paper employs a weighted network approach to study the empirical properties of the web of trade relationships among world countries, and its evolution over time. We show that most countries are characterized by weak trade links; yet,…
A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free…
A model for the spread of an infection is analyzed for different population structures. The interactions within the population are described by small world networks, ranging from ordered lattices to random graphs. For the more ordered…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters)…
This paper presents an evolution model of weighted networks in which the structural growth and weight dynamics are driven by human behavior, i.e. passenger route choice behavior. Transportation networks grow due to people's increasing…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
Wireless Sensor Networks (WSNs) have become widely used in various fields like environmental monitoring, smart agriculture, and health care. However, their extensive usage also introduces significant vulnerabilities to cyber viruses.…
Knowing which parts of a complex system have identical roles simplifies computations and reveals patterns in its network structure. Group theory has been applied to study symmetries in unweighted networks. However, in real-world weighted…
We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…
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,…
A very interesting matter of Network Science is assessing how complex a given network is. In other words, by how much does such a network departs from any general patterns which could be evoked for its description. Among other choices,…
A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such…
Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
The weight of links in a network is often related to the similarity of the nodes. Here, we introduce a simple tunable measure for analysing the similarity of nodes across different link weights. In particular, we use the measure to analyze…