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Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…
In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…
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…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place.…
The way in which different types of dynamics unfold in complex networks is intrinsically related to the propagation of activation along nodes, which is strongly affected by the network connectivity. In this work we investigate to which…
Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
Social network structure is very important for understanding human information diffusing, cooperating and competing patterns. It can bring us with some deep insights about how people affect each other. As a part of complex networks, social…
The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e.…
We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular…
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…
We study the performance of Weibull and scale free Internet-like networks and compare them to a classical random graph based network. The scaling of the traffic load with the nodal degree is established, and confimed in a numerical…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions have the power-law form. In this paper, we investigate the synchronization phenomena in a scale-free…
Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability, theoretical computer science, network science, and machine…
Quantum walks have frequently envisioned the behavior of a quantum state traversing a classically defined, generally finite, graph structure. While this approach has already generated significant results, it imposes a strong assumption: all…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…
Diffusion models degrade images through noise, and reversing this process reveals an information hierarchy across timesteps. Scale-space theory exhibits a similar hierarchy via low-pass filtering. We formalize this connection and show that…
We study the random walk problem on a class of deterministic Scale-Free networks displaying a degree sequence for hubs scaling as a power law with an exponent $\gamma=\log 3/\log2$. We find exact results concerning different first-passage…