Related papers: The connectivity-profile of random increasing k-tr…
The present study was concerned with network failure problems for simple connected undirected graphs. A connected graph becomes unconnected through edge failure, under the assumptions that only edges can fail and each edge has an identical…
We explore the interplay between the topological relevance of a neuron and its dynamical traces in experimental cultured neuronal networks. We monitor the growth and development of these networks to characterise the evolution of their…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme of node reinforcement can be considered as a benchmark for finding an…
A k-ranking of a graph G is a labeling of the vertices of G with values from {1,...,k} such that any path joining two vertices with the same label contains a vertex having a higher label. The tree-depth of G is the smallest value of k for…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
We investigate a variety of statistical properties associated with the number of distinct degrees that exist in a typical network for various classes of networks. For a single realization of a network with N nodes that is drawn from an…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
This article discusses random hypergraphs with varying hyperedge sizes, admitting large hyperedges with size tending to infinity, and heavy-tailed limiting hyperedge size distributions. The main result describes a threshold for the random…
A learning algorithm is presented which given the structure of a causal tree, will estimate its link probabilities by sequential measurements on the leaves only. Internal nodes of the tree represent conceptual (hidden) variables…
We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the p-th power of the in-degree of b. We restrict to the…
A k-ranking of a graph G is a labeling of the vertices of G with values from {1,...,k} such that any path joining two vertices with the same label contains a vertex having a higher label. The tree-depth of G is the smallest value of k for…
Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…
Recently, graphs have been widely used to represent many different kinds of real world data or observations such as social networks, protein-protein networks, road networks, and so on. In many cases, each node in a graph is associated with…
This paper investigates the addition of random edges to arbitrary dense graphs; in particular, we determine the number of random edges required to ensure various monotone properties including the appearance of a fixed size clique, small…
We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations,…
This paper presents an approach to the modeling of degree-degree correlation in complex networks. Thus, a simple function, \Delta(k', k), describing specific degree-to- degree correlations is considered. The function is well suited to…
A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be…
Regression trees have emerged as a preeminent tool for solving real-world regression problems due to their ability to deal with nonlinearities, interaction effects and sharp discontinuities. In this article, we rather study regression trees…