Related papers: Range-based attacks on links in random scale-free …
We investigate site percolation in a hierarchical scale-free network known as the Dorogovtsev- Goltsev-Mendes network. We use the generating function method to show that the percolation threshold is 1, i.e., the system is not in the…
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)…
In this article, we proposed a susceptible-infected model with identical infectivity, in which, at every time step, each node can only contact a constant number of neighbors. We implemented this model on scale-free networks, and found that…
We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the…
The statistical modeling of random networks has been widely used to uncover interaction mechanisms in complex systems and to predict unobserved links in real-world networks. In many applications, network connections are collected via…
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…
Developing autonomous agents that can interact with changing environments is an open challenge in machine learning. Robustness is particularly important in these settings as agents are often fit offline on expert demonstrations but deployed…
The capacity to resist attacks from the environment is crucial to the survival of all organisms. We quantitatively analyze the susceptibility of protein interaction networks of numerous organisms to random and malicious attacks. We find for…
The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering…
Cascading breakdowns of real networks are severe accidents in recent years, such as the blackouts of the power transportation networks in North America. In this paper, we study the effects of geographical structure on the cascading…
Extensive researches have been dedicated to investigating the performance of real networks and synthetic networks against random failures or intentional attack guided by degree (degree attack). Degree is one of straightforward measures to…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
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…
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 spectrum of network is an important tool to study the function and dynamic properties of network, and graph operation and product is an effective mechanism to construct a specific local and global topological structure. In this study, a…
Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing…
Cascading failures, wherein the failure of one component triggers subsequent failures in complex interconnected systems, pose a significant risk of disruptions and emerge across various domains. Understanding and mitigating the risk of such…
A new mechanism leading to scale-free networks is proposed in this letter. It is shown that in many cases of interest, the connectivity power-law behavior is neither related to dynamical properties nor to preferential attachment. Instead,…
Link prediction is one of the fundamental problems in computational social science. A particularly common means to predict existence of unobserved links is via structural similarity metrics, such as the number of common neighbors; node…
Many real networks such as the World Wide Web, financial, biological, citation and social networks have a power-law degree distribution. Networks with this feature are also called scale-free. Several models for producing scale-free networks…