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Generative methods for graphs need to be sufficiently flexible to model complex dependencies between sets of nodes. At the same time, the generated graphs need to satisfy domain-dependent feasibility conditions, that is, they should not…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
We introduce a novel preferential attachment model using the draw variables of a modified P\'olya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
The preferential attachment (PA) model is a popular way of modeling dynamic social networks, such as collaboration networks. Assuming that the PA function takes a parametric form, we propose and study the maximum likelihood estimator of the…
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…
The trapping problem on graph (or network) as a typical focus of great interest has attracted more attention from various science fields, including applied mathematics and theoretical computer science, in the past. Here, we first study this…
Semi-random processes involve an adaptive decision-maker, whose goal is to achieve some predetermined objective in an online randomized environment. They have algorithmic implications in various areas of computer science, as well as…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
The graphical balls-into-bins process is a generalization of the classical 2-choice balls-into-bins process, where the bins correspond to vertices of an arbitrary underlying graph $G$. At each time step an edge of $G$ is chosen uniformly at…
Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features…
Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…
We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to have partitions with linearly many pieces of bounded size, we…
Graph refinement, or the task of obtaining subgraphs of interest from over-complete graphs, can have many varied applications. In this work, we extract trees or collection of sub-trees from image data by, first deriving a graph-based…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
A vertex of a randomly growing graph is called a persistent hub if at all but finitely many moments of time it has the maximal degree in the graph. We establish the existence of a persistent hub in the Barab\'asi--Albert random graph model…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
Many dynamic processes such as telecommunication and transport networks can be described through discrete time series of graphs. Modelling the dynamics of such time series enables prediction of graph structure at future time steps, which…