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About 4,966 papers for “Preferential attachment”

Quantum preferential attachment

Tingyu Zhao, Balázs Maga, Pierfrancesco Dionigi et al. · ArXiv.org · 2025

The quantum internet is a rapidly developing technological reality, yet, it remains unclear what kind of quantum network structures might emerge. Since indirect quantum communication is already feasible and preserves absolute security of the communication channel, a new node joining the quantum network does not need to connect directly to its desired target. Instead, in our proposed quantum preferential attachment model, it uniformly randomly connects to any node within the proximity of the target, including, but not restricted to, the target itself. This local flexibility is found to qualitatively change the global network behavior, leading to two distinct classes of complex network architectures, both of which are small-world, but neither of which is scale-free. Our numerical findings are supported by rigorous analytic results, in a framework that incorporates quantum and classical variants of preferential attachment in a unified phase diagram. Besides quantum networks, we expect that our results will have broad implications for classical scenarios where there is flexibility in establishing new connections.

Cited by 0Open access

Random Preferential Attachment Hypergraphs

Chen Avin, Zvi Lotker, David Peleg · arXiv (Cornell University) · 2015

The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment evolution model than by the ordinary (uniform) evolution lodel. Analogously, this paper extends the random {\em hypergraph} model to a random {\em preferential attachment hypergraph} model. We then analyze the degree distribution of random preferential attachment hypergraphs and show that they possess heavy tail degree distribution properties similar to those of random preferential attachment graphs. However, our results show that the exponent of the degree distribution is sensitive to whether one considers the structure as a hypergraph or as a graph.

Cited by 3Open access

Self-Reinforced Preferential Attachment

Dahiya, Yogesh, Hollander, Frank den · ArXiv.org · 2025

We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all prior times. The resulting growing graph is a random tree whose vertices have degrees that grow polynomially fast in time. We compute the growth exponent, show that it is strictly larger than the growth exponent in the absence of self-reinforcement, and develop insight into how the self-reinforcement affects the growth. Proofs are based on a stochastic approximation scheme.

Cited by 0Open access

Succinct Preferential Attachment Graphs

Ziad Ismaili Alaoui, Namrata Namrata, Sebastian Wild · ArXiv.org · 2025

Computing over compressed data combines the space saving of data compression with efficient support for queries directly on the compressed representation. Such data structures are widely applied in text indexing and have been successfully generalised to trees. For graphs, support for computing over compressed data remains patchy; typical results in the area of succinct data structures are restricted to a specific class of graphs and use the same, worst-case amount of space for any graph from this class. In this work, we design a data structure whose space usage automatically improves with the compressibility of the graph at hand, while efficiently supporting navigational operations (simulating adjacency-list access). Specifically, we show that the space usage approaches the instance-optimal space when the graph is drawn according to the classic Barabási-Albert model of preferential-attachment graphs. Our data-structure techniques also work for arbitrary graphs, guaranteeing a size asymptotically no larger than an entropy-compressed edge list. A key technical contribution is the careful analysis of the instance-optimal space usage.

Cited by 0Open access

Self-reinforced preferential attachment

Yogesh Dahiya, Frank den Hollander · Electronic Communications in Probability · 2026

We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all prior times. The resulting growing graph is a random tree whose vertices have degrees that grow polynomially fast in time. We compute the growth exponent, show that it is strictly larger than the growth exponent in the absence of self-reinforcement, and develop insight into how the self-reinforcement affects the growth. Proofs are based on a stochastic approximation scheme.

Cited by 0Open access

Preferential attachment random graphs

Hopmans, HA Rik · TU/e Research Portal (Eindhoven University of Technology) · 2013

In the modern world there are many networks, some complex networks like the internet or social networks like communities of people. A specific network is investigated in this thesis since a network can be represented mathematically by a graph. The so-called preferential attachment random graph is also called the rich-get-richer model and is a social network. In this social network one is more likely to know a person who already knows many people. That form of attachment is represented in the preferential attachment random graph. Networks like this social network often satisfy two main properties, they are scale-free and small worlds. The distance between elements of the network determines how the network is connected. The distances in the preferential attachment graph are determined by simulations in this thesis. The results for the distances are compared with the distances of the configuration model. The average distance in the preferential attachment graph stays small, when the network grows larger with a factor of 10, the average distance in the graph grows logarithmic or even less.

Cited by 0

Preferential attachment with choice

John Haslegrave, Jonathan Jordan · Random Structures and Algorithms · 2015

We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses vertices according to a preferential rule and connects to the vertex in the selection with the th highest degree. For meek choice, where , we show that both double exponential decay of the degree distribution and condensation-like behaviour are possible, and provide a criterion to distinguish between them. For greedy choice, where , we confirm that the degree distribution asymptotically follows a power law with logarithmic correction when and shows condensation-like behaviour when . © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 751–766, 2016

Cited by 17Open access

Exponents and for preferential creation and preferential attachment.

Peng Zhang (2071), Menghui Li (527095), Liang Gao (368796) et al. · Figshare · 2015

<p>Exponents and as in , which characterize the influence of current degree of activity and degree of popularity on the formation of cross links between existing users and existing items as well as the formation of cross links between existing users (items) and new items (user) [in the brackets] The results are averaged over 10 randomly selected snapshots, where the exponents are determined by least-square fitting, and generally.</p>

Cited by 0Open access

The origin of preferential attachment and the generalized preferential attachment for weighted networks

Chen, Chen · arXiv (Cornell University) · 2006

In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network, which makes it is neither entirely degree preferential nor entirely weight preferential. Second, it can tell us not only the chance that each already-existing vertex being connected but also how much weight each new edge has. The generalized preferential attachment can generate four power-law distributions, besides the three for vertex degrees, vertex strengths, and edge weights, it yield a new power-law distribution for the subgraph degrees.

Cited by 0Open access

Robustness of preferential-attachment graphs

Rouzbeh Hasheminezhad, Ulrik Brandes · Applied Network Science · 2023

Abstract The widely used characterization of scale-free networks as “robust-yet-fragile” originates primarily from experiments on instances generated by preferential attachment. According to this characterization, scale-free networks are more robust against random failures but more fragile against targeted attacks when compared to random networks of the same size. Here, we consider a more appropriate baseline by requiring that the random networks match not only the size but also the inherent minimum degree of preferential-attachment networks they are compared with. Under this more equitable condition, we can (1) prove that random networks are almost surely robust against any vertex removal strategy and (2) show through extensive experiments that scale-free networks generated by preferential attachment are not particularly robust against random failures. Finally, we (3) add experiments demonstrating that preferentially attaching to well-connected vertices does not enhance robustness at all.

Cited by 5Open access

Coexistence in preferential attachment networks

Antunović, Tonći, Mossel, Elchanan, Racz, Miklos Z. · arXiv (Cornell University) · 2013

We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses neighbours by preferential attachment, and selects its type based on the number of initial neighbours of each type. The model is analysed in detail, and in particular, we determine the possible proportions of the various types in the limit of large networks. An important qualitative feature we find is that, in contrast to many current theoretical models, often several competitors will coexist. This matches empirical observations in many real-world networks.

Cited by 0Open access

Preferential attachment in sexual networks

Birgitte Freiesleben de Blasio, Åke Svensson, Fredrik Liljeros · Proceedings of the National Academy of Sciences · 2007

Many social networks are characterized by a highly uneven distribution of links. The observed skewed distributions have in several cases been attributed to preferential attachment (PA), a tendency among nodes in a growing network to form new links preferentially to nodes with high numbers of links. We test the PA conjecture in sexual contact networks. A maximum likelihood estimation-based expectation-maximization fitting technique is used to model new partners over a 1-year period based on the number of partners in foregoing periods of 2 years, 4 years, and lifetime. The PA model is modified to account for individual heterogeneity in the inclination to find new partners and fitted to Norwegian survey data on heterosexual men and women. Results show evidence of nonrandom, sublinear PA when comparing the growth in 3- to 5-year periods. The potential implications of these findings are discussed.

Cited by 60Open access

Compression of Preferential Attachment Graphs

Tomasz Łuczak, Abram Magner, Wojciech Szpankowski · 2019

We study structural properties of preferential attachment graphs (with parameter m ≥ 1 giving the number of attachment choices that each new vertex makes) which intervene in two complementary algorithmic/statistical/information-theoretic problems involving the information shared between a random graph's labels and its structure: in structural compression, we seek to compactly describe a graph's structure by a bit string, throwing away its label information; in node arrival order recovery, we seek to recover node labels, given only a graph structure. In particular, we study the typical size of the automorphism group, as well as some shape parameters (such as the number of linear extensions and height) of the directed version of the graph, which in turn allows us to estimate the typical number of admissible labeled representatives of a given graph structure. Our result on the automorphism group positively settles a conjecture to the effect that, provided that m ≥ 3, preferential attachment graphs are asymmetric with high probability, and completes the characterization of the number of symmetries for a broad range of parameters of the model (i.e., for all fixed m). These results allow us to give an algorithmically efficient, asymptotically optimal algorithm for compression of unlabeled preferential attachment graphs. To show the optimality of our scheme, we also derive new, precise estimates of the Shannon entropy of both the unlabeled and labeled version of the model. Our results also imply inapproximability results for the problem of node arrival order recovery.

Cited by 14

De-Preferential Attachment Random Graphs

Bandyopadhyay, Antar, Sen, Subhabrata · ArXiv.org · 2025

In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied \emph{preferential attachment random graphs} \cite{BarAlb99}, we call such a sequence a \emph{de-preferential attachment random graph model}. We consider two types of models, namely, \emph{inverse de-preferential}, where the attachment probabilities are inversely proportional to the degree and \emph{linear de-preferential}, where the attachment probabilities are proportional to $c-$degree, where $c > 0$ is a constant. For the case when each new vertex comes with exactly one half-edge we show that the degree of a fixed vertex is asymptotically of the order $\sqrt{\log n}$ for the inverse de-preferential case and of the order $\log n$ for the linear case. These show that compared to preferential attachment, the degree of a fixed vertex grows to infinity at a much slower rate for these models. We also show that in both cases limiting degree distributions have exponential tails. In fact we show that for the inverse de-preferential model the tail of the limiting degree distribution is faster than exponential while that for the linear de-preferential model is exactly the $\mbox{Geometric}\left(\frac{1}{2}\right)$ distribution. For the case when each new vertex comes with $m > 1$ half-edges, we show that similar asymptotic results hold for fixed vertex degree in both inverse and linear de-preferential models. Our proofs make use of the martingale approach as well as embedding to certain continuous time age dependent branching processes.

Cited by 0Open access