Related papers: Higher-order distributions and nongrowing complex …
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)…
We generalize the degree-organizational view of real-world networks with broad degree-distributions in a landscape analogue with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent…
We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration $t_w$ and random long-range jumps. While the time the walker needs to cover all the…
We define gradient networks as directed graphs formed by local gradients of a scalar field distributed on the nodes of a substrate network G. We derive an exact expression for the in-degree distribution of the gradient network when the…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
In this paper, a simply rule that generates scale-free networks with very large clustering coefficient and very small average distance is presented. These networks are called {\bf Multistage Random Growing Networks}(MRGN) as the adding…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous…
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…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…
Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…
A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…
Uncorrelated random scale-free networks are useful null models to check the accuracy an the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable to generate random uncorrelated…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
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…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
Although the analysis of loops is not so much because of the complications, it has already been found that heuristically enhancing loops decreases the variance of degree distributions for improving the robustness of connectivity. While many…
Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…