A Dynamic Model for On-Line Social Networks

Bonato, Anthony; Hadi, Noor; Horn, Paul; Prałat, Paweł; Wang, Changping

doi:10.1007/978-3-540-95995-3_11

Cited by 19 publications

(12 citation statements)

References 27 publications

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“…Tribe ID OD C CON B Richard Tagi 6 Note that Richard, the Sole Survivor of the season, has one of the highest closeness and CON scores. Rudy and Susan have higher scores, however.…”

Section: Namementioning

confidence: 99%

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Dynamic Competition Networks: Detecting Alliances and Leaders

Bonato

Eikmeier

Gleich

et al. 2018

Lecture Notes in Computer Science

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We consider social networks of competing agents that evolve dynamically over time. Such dynamic competition networks are directed, where a directed edge from nodes u to v corresponds a negative social interaction. We present a novel hypothesis that serves as a predictive tool to uncover alliances and leaders within dynamic competition networks. Our focus is in the present study is to validate it on competitive networks arising from social game shows such as Survivor and Big Brother.

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“…Tribe ID OD C CON B Richard Tagi 6 Note that Richard, the Sole Survivor of the season, has one of the highest closeness and CON scores. Rudy and Susan have higher scores, however.…”

Section: Namementioning

confidence: 99%

“…Competitive relationships were studied recently via the Iterated Local Anti-Transitivity (or ILAT) model; see [6,7]. In the ILAT model, each node u duplicates every time-step by forming its anti-clone u ′ , so that u ′ joins to the nodes in the non-neighbor set of u.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Competition Networks: Detecting Alliances and Leaders

Bonato

Eikmeier

Gleich

et al. 2018

Lecture Notes in Computer Science

Self Cite

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“…. A M as defined in equations (9) and (10). We consider canonical paths containing e that run between every possible pair of sets in this partition.…”

Section: The Mixing Time For Gtgmentioning

confidence: 99%

On the mixing time of geographical threshold graphs

Beveridge

Bradonjic²

2011

Discrete Mathematics

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We study the mixing time of random graphs in the d-dimensional toric unit cube [0, 1] d generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights, drawn from some distribution. The connectivity threshold for GTGs is comparable to that of RGGs, essentially corresponding to a connectivity radius of r = (log n/n) 1/d . However, the degree distributions at this threshold are quite different: in an RGG the degrees are essentially uniform, while RGGs have heterogeneous degrees that depend upon the weight distribution. Herein, we study the mixing times of random walks on d-dimensional GTGs near the connectivity threshold for d ≥ 2. If the weight distribution function decays with P[W ≥ x] = O(1/x d+ν ) for an arbitrarily small constant ν > 0 then the mixing time of GTG is O(n 2/d (log n) (d−2)/d ). This matches the known mixing bounds for the d-dimensional RGG.

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“…The Iterated Local Transitivity (ILT ) model introduced in [11,12] and further studied in [8,9,25], simulates structural properties in complex networks emerging from transitivity. Transitivity gives rise to the notion of cloning, where an introduced vertex x is adjacent to all of the neighbors of some pre-existing vertex y.…”

Section: Introductionmentioning

confidence: 99%

The iterated local transitivity model for hypergraphs

Behague¹,

Bonato²,

Huggan³

et al. 2021

Preprint

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Complex networks are pervasive in the real world, capturing dyadic interactions between pairs of vertices, and a large corpus has emerged on their mining and modeling. However, many phenomena are comprised of polyadic interactions between more than two vertices. Such complex hypergraphs range from emails among groups of individuals, scholarly collaboration, or joint interactions of proteins in living cells. Complex hypergraphs and their models form an emergent topic, requiring new models and techniques.A key generative principle within social and other complex networks is transitivity, where friends of friends are more likely friends. The previously proposed Iterated Local Transitivity (ILT) model incorporated transitivity as an evolutionary mechanism. The ILT model provably satisfies many observed properties of social networks, such as densification, low average distances, and high clustering coefficients.We propose a new, generative model for complex hypergraphs based on transitivity, called the Iterated Local Transitivity Hypergraph (or ILTH) model. In ILTH, we iteratively apply the principle of transitivity to form new hypergraphs. The resulting model generates hypergraphs simulating properties observed in real-world complex hypergraphs, such as densification and low average distances. We consider properties unique to hypergraphs not captured by their 2-section. We show that certain motifs, which are specified subhypergraphs of small order, have faster growth rates in ILTH hypergraphs than in random hypergraphs with the same order and expected average degree. We show that the graphs admitting a homomorphism into the 2-section of the initial hypergraph appear as induced subgraphs in the 2-section of ILTH hypergraphs. We consider new and existing hypergraph clustering coefficients, and show that these coefficients have larger values in ILTH hypergraphs than in comparable random hypergraphs.

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A Dynamic Model for On-Line Social Networks

Cited by 19 publications

References 27 publications

Dynamic Competition Networks: Detecting Alliances and Leaders

Dynamic Competition Networks: Detecting Alliances and Leaders

On the mixing time of geographical threshold graphs

The iterated local transitivity model for hypergraphs

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