A Hypergraph Approach for Estimating Growth Mechanisms of Complex Networks

Inoue, Masatoshi; Pham, Thong; Shimodaira, Hidetoshi

doi:10.1109/access.2022.3143612

Cited by 3 publications

(2 citation statements)

References 42 publications

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“…In Capocci et al (2006), properties of Wikipedia are studied by representing topics as vertices and hyperlinks between them as edges. Several preferential attachment hypergraphs (i.e., graphs in which an edge can join any number of vertices) generating models have also been devised in the literature (Avin et al, 2019;Giroire et al, 2022;Inoue et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

Generating preferential attachment graphs via a Pólya urn with expanding colors

Singh,

Alajaji,

Gharesifard

2024

Net Sci

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We introduce a novel preferential attachment model using the draw variables of a modified Pólya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph evolves. Similar to the Barabási-Albert model, the generated graph grows in size by one vertex at each time instance; in contrast however, each vertex of the graph is uniquely characterized by a color, which is represented by a ball color in the Pólya urn. More specifically at each time step, we draw a ball from the urn and return it to the urn along with a number of reinforcing balls of the same color; we also add another ball of a new color to the urn. We then construct an edge between the new vertex (corresponding to the new color) and the existing vertex whose color ball is drawn. Using color-coded vertices in conjunction with the time-varying reinforcing parameter allows for vertices added (born) later in the process to potentially attain a high degree in a way that is not captured in the Barabási-Albert model. We study the degree count of the vertices by analyzing the draw vectors of the underlying stochastic process. In particular, we establish the probability distribution of the random variable counting the number of draws of a given color which determines the degree of the vertex corresponding to that color in the graph. We further provide simulation results presenting a comparison between our model and the Barabási-Albert network.

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Section: Introductionmentioning

confidence: 99%

Generating preferential attachment graphs via a Pólya urn with expanding colors

Singh,

Alajaji,

Gharesifard

2024

Net Sci

View full text Add to dashboard Cite

show abstract

“…In [14], properties of Wikipedia are studied by representing topics as vertices and hyperlinks between them as edges. Several preferential attachment hypergraphs (i.e., graphs in which an edge can join any number of vertices) generating models have also been devised in the literature [15], [16], [17].…”

Section: Introductionmentioning

confidence: 99%

Modeling Network Contagion Via Interacting Finite Memory Pólya Urns

Singh

Alajaji

Gharesifard

2022

2022 IEEE International Symposium on Information Theory (ISIT)

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We introduce a novel preferential attachment model using the draw variables of a modified Pólya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph evolves. Similar to the Barabási-Albert model, the generated graph grows in size by one vertex at each time instance; in contrast however, each vertex of the graph is uniquely characterized by a color, which is represented by a ball color in the Pólya urn. More specifically at each time step, we draw a ball from the urn and return it to the urn along with a number (potentially time-varying and non-integer) of reinforcing balls of the same color; we also add another ball of a new color to the urn. We then construct an edge between the new vertex (corresponding to the new color) and the existing vertex whose color ball is drawn. Using color-coded vertices in conjunction with the time-varying reinforcing parameter allows for vertices added (born) later in the process to potentially attain a high degree in a way that is not captured in the Barabási-Albert model. We study the degree count of the vertices by analyzing the draw vectors of the underlying stochastic process. In particular, we establish the probability distribution of the random variable counting the number of draws of a given color which determines the degree of the vertex corresponding to that color in the graph. We further provide simulation results presenting a comparison between our model and the Barabási-Albert network.

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Dynamical evolution behavior of scientific collaboration hypernetwork

Wang

Wei

2022

AIP Advances

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Scientific collaboration has a complex hypernetwork structure. How to construct scientific collaboration in a complex system is an open issue. In this paper, a non-uniform dynamic collaborative evolution model is proposed. In the proposed method, each scholar is viewed as a node, and each cooperation relationship is regarded as a hyperedge. This model includes three processes: adding hyperedges, entering nodes, and forming hyperedges by new nodes. It is theoretically proved that the hyperdegree distribution of nodes follows the power law distribution. Furthermore, the effects of different parameters on the proposed model are numerically simulated in this paper. The experimental results are consistent with the theoretical ones. In addition, experiments show that the influence of nodes and hyperedges will affect the selection of old nodes when new nodes enter the network. This paper not only considers the construction of hyperedges with old nodes but also considers the possibility that new nodes construct new hyperedges among themselves. This model provides a reference for the research of the evolution process of scientific collaboration hypernetworks.

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A Hypergraph Approach for Estimating Growth Mechanisms of Complex Networks

Cited by 3 publications

References 42 publications

Generating preferential attachment graphs via a Pólya urn with expanding colors

Generating preferential attachment graphs via a Pólya urn with expanding colors

Modeling Network Contagion Via Interacting Finite Memory Pólya Urns

Dynamical evolution behavior of scientific collaboration hypernetwork

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