Related papers: Persistence of centrality in random growing trees

In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…

We study structural properties of trees grown by preferential attachment. In this mechanism, nodes are added sequentially and attached to existing nodes at a rate that is strictly proportional to the degree. We classify nodes by their depth…

We determine the tree which maximizes the distance between characteristic set and subtree core over all trees on $n$ vertices. The asymptotic nature of this distance is also discussed. The problem of extremizing the distance between…

We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…

Random planar graphs appear in a variety of context and it is important for many different applications to be able to characterize their structure. Local quantities fail to give interesting information and it seems that path-related…

We show that the growth of a unimodular random rooted tree $(T,o)$ of degree bounded by $d$ always exists, assuming its upper growth passes the critical threshold $\sqrt{d-1}$. This complements Timar's work who showed the possible…

We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node's position in the network. This enables us to provide a taxonomy of centrality…

For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem…

We use the framework of multivariate regular variation to analyse the extremal behaviour of preferential attachment models. To this end, we follow a directed linear preferential attachment model for a random, heavy-tailed number of steps in…

We introduce a model of evolving preferential attachment trees where vertices are assigned weights, and the evolution of a vertex depends not only on its own weight, but also on the weights of its neighbours. We study the distribution of…

A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…

The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…

Betweenness centrality of a vertex in a graph measures the fraction of shortest paths going through the vertex. This is a basic notion for determining the importance of a vertex in a network. The k-betweenness centrality of a vertex is…

In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…

The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings…

Models of growing networks are a central topic in network science. In these models, vertices are usually labeled by their arrival time, distinguishing even those node pairs whose structural roles are identical. In contrast, unlabeled…