Influence of the seed in affine preferential attachment trees

@article{Marchand2018InfluenceOT,
  title={Influence of the seed in affine preferential attachment trees},
  author={David Marchand and Ioan Manolescu},
  journal={arXiv: Probability},
  year={2018}
}
We study randomly growing trees governed by the affine preferential attachment rule. Starting with a seed tree $S$, vertices are attached one by one, each linked by an edge to a random vertex of the current tree, chosen with a probability proportional to an affine function of its degree. This yields a one-parameter family of preferential attachment trees $(T_n^S)_{n\geq|S|}$, of which the linear model is a particular case. Depending on the choice of the parameter, the power-laws governing the… Expand
1 Citations

Figures from this paper

A Cluster Model for Growth of Random Trees
We first consider the growth of trees by probabilistic attachment of new vertices to leaves. This leads to a growth model based on vertex clusters and probabilities assigned to clusters. This modelExpand

References

SHOWING 1-10 OF 18 REFERENCES
Finding Adam in random growing trees
TLDR
Algorithms to find the first vertex in large trees generated by either the uniform attachment or preferential attachment model are investigated, and it is shown that for any $\epsilon$, there exist algorithms with $K$ independent of the size of the input tree. Expand
Scaling limits and influence of the seed graph in preferential attachment trees
TLDR
As the number of nodes grows, it is shown that these looptrees, appropriately rescaled, converge in the Gromov-Hausdor sense towards a random compact metric space which the authors call the Brownian looptree. Expand
On the Influence of the Seed Graph in the Preferential Attachment Model
TLDR
A first step in proving the conjecture that different seeds lead to different distributions of limiting trees from a total variation point of view is taken, showing that seeds with different degree profiles Lead to different limiting distributions for the (appropriately normalized) maximum degree. Expand
Connectivity Transitions in Networks with Super-Linear Preferential Attachment
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 pth power ofExpand
Finding the seed of uniform attachment trees
A uniform attachment tree is a random tree that is generated dynamically. Starting from a fixed "seed" tree, vertices are added sequentially by attaching each vertex to an existing vertex chosenExpand
Universal techniques to analyze preferential attachment trees : Global and Local analysis
We use embeddings in continuous time Branching processes to derive asymptotics for various statistics associated with different models of preferential attachment. This powerful method allows us toExpand
From trees to seeds: on the inference of the seed from large trees in the uniform attachment model
TLDR
It is shown that different seeds lead to different distributions of limiting trees from a total variation point of view, and statistics are constructed that measure, in a certain well-defined sense, global "balancedness" properties of such trees. Expand
On the discovery of the seed in uniform attachment trees
We investigate the size of vertex confidence sets for including part of (or the entirety of) the seed in seeded uniform attachment trees, given knowledge of some of the seed's properties, and with aExpand
The degree sequence of a scale-free random graph process
TLDR
Here the authors obtain P(d) asymptotically for all d≤n1/15, where n is the number of vertices, proving as a consequence that γ=3.9±0.1 is obtained. Expand
Connectivity of growing random networks.
TLDR
A solution for the time- and age-dependent connectivity distribution of a growing random network is presented and the power law N(k) approximately k(-nu) is found, where the exponent nu can be tuned to any value in the range 2. Expand
...
1
2
...