Related papers: Revisiting Degree Distribution Models for Social G…

Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…

Power system studies require the topological structures of real-world power networks; however, such data is confidential due to important security concerns. Thus, power grid synthesis (PGS), i.e., creating realistic power grids that imitate…

We study a modified version of a model previously proposed by Jackson and Wolinsky to account for communicating information and allocating goods in socioeconomic networks. In the model, the utility function of each node is given by a…

Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at…

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…

This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood…

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…

We investigate scaling properties of human brain functional networks in the resting-state. Analyzing network degree distributions, we statistically test whether their tails scale as power-law or not. Initial studies, based on least-squares…

Heterophilic Graph Neural Networks (HGNNs) have shown promising results for semi-supervised learning tasks on graphs. Notably, most real-world heterophilic graphs are composed of a mixture of nodes with different neighbor patterns,…

In this paper, we propose a new graph sampling method for online social networks that achieves the following. First, a sample graph should reflect the ratio between the number of nodes and the number of edges of the original graph. Second,…

We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…

The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…

Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs).…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…

Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…

Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured…

There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…

We investigate the asymptotic number of induced subgraphs in power-law uniform random graphs. We show that these induced subgraphs appear typically on vertices with specific degrees, which are found by solving an optimization problem.…

Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…