Related papers: Asymptotic degree distributions in random threshol…

We generalize the asymptotic behavior of the graph distance between two uniformly chosen nodes in the configuration model to a wide class of random graphs. Among others, this class contains the Poissonian random graph, the expected degree…

We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…

The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…

The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…

A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…

Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical…

It is often claimed that the entropy of a network's degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former…

The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not…

Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…

We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…

We investigate the statistics of the most connected nodes in scale-free networks. For a scale-free network model with homogeneous nodes, we show by means of extensive simulations that the exponential truncation--due to the finite size of…

Despite great effort spent measuring topological features of large networks like the Internet, it was recently argued that sampling based on taking paths through the network (e.g., traceroutes) introduces a fundamental bias in the observed…

This paper investigates the limiting behaviour of degree-degree correlation metrics for sequences of random graphs under a general assumption of local convergence in probability. We establish convergence results for Pearson's correlation…

We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…

In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large…

Two node variables determine the evolution of cascades in random networks: a node's degree and threshold. Correlations between both fundamentally change the robustness of a network, yet, they are disregarded in standard analytic methods as…

We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…

We establish limit theorems that describe the asymptotic local and global geometric behaviour of random enriched trees considered up to symmetry. We apply these general results to random unlabelled weighted rooted graphs and uniform random…

The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in…