Related papers: Rigorous results on the threshold network model
Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
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…
Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in…
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…
Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…
In order to take the weight of connection into consideration and to find a natural measurement of weight, we have collected papers in Econophysics and constructed a network of scientific communication to integrate idea transportation among…
This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on…
The apparent disconnection between the microscopic and the macroscopic is a major issue in the understanding of complex systems. To this extend, we study the convergence of repeatedly applying local rules on a network, and touch on the…
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
Complex networks are made up of vertices and edges. The latter connect the vertices. There are several ways to measure the importance of the vertices, e.g., by counting the number of edges that start or end at each vertex, or by using the…
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…
Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the…
Let $X_1,X_2,...$ be an infinite sequence of i.i.d. random vectors distributed exponentially with parameter $\lam .$ For each $y$ and $n\geq 1,$ form a graph $G_n(y)$ with vertex set $V_n = \{X_1,...,X_n\},$ two vertices are connected if…
Image classification based on over-parametrized convolutional neural networks with a global average-pooling layer is considered. The weights of the network are learned by gradient descent. A bound on the rate of convergence of the…