Generalized graph products for network design and analysis

Parsonage, Eric; Nguyen, Hung; Bowden, Rhys; Knight, Simon; Falkner, Nickolas; Roughan, Matthew

doi:10.1109/icnp.2011.6089084

Cited by 21 publications

(22 citation statements)

References 22 publications

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“…The former requires a structured approach mimicking the design rules used by network engineers, which can be expressed through graph products [25]. The latter requires elements of geography and traffic optimisation as expressed in COLD, but routing policy is also more complicated than the shortest-path routing used here.…”

Section: Resultsmentioning

confidence: 99%

“…It generates link capacities and distances along with routing. 6. The PoP-level model has only four parameters, and we show why at least this many are needed.…”

Section: Background and Comparisonsmentioning

confidence: 98%

“…• this is the level at which many of the interesting problems lie (the generation of the router-level network from the PoP level can be easily accomplished using either existing probabilistic methods [5], or structural methods [6]); • networks change less frequently at the PoP level than at the router level [7]; and • the PoP level is the more interesting level for many activities [7], because it is less dependent on the details of protocol implementations, router vendor and model, and other technological details. The last point is subtle but important.…”

Section: -Attributed To a Einsteinmentioning

confidence: 99%

“…COLD satisfies these requirements. The key is choosing a synthesis process that parallels the real network design used by many network engineers, i.e., heuristic optimization of economic and demographic objectives and constraints, followed by templated design to implement physical routerlevel structures within PoPs (see [6] for example), mimicking the highly structured and pattern-based methods recommended in basic texts on network management [2][3][4]. Likewise, simple heuristics can be used to create interdomain connectivity between networks if such is needed.…”

Section: A Network's Form Is Driven By Real Costs and Technicalmentioning

confidence: 99%

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Cold

Bowden

Roughan

Bean

2014

Proceedings of the 10th ACM International on Conference on Emerging Networking Experiments and Technologies

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Network topology synthesis seeks methods to generate large numbers of example network topologies primarily for use in simulation. It is a topic that has received much attention over the years, underlying which is a conflict between randomness and design. Random graphs are appealing because they are simple and avoid the messy details that plague real networks. However real networks are messy, because network operators design their networks in the context of complex technological constraints, costs, and goals. When random models have been used they often produce patently unrealistic networks that only match a few artificial connectivity statistics of real networks: the features that make the network useful and interesting are ignored. At best a network divorced from context is a purely mathematical object with no meaning or utility. At worst it can be completely misleading. However, design alone cannot generate an ensemble of networks with the variability needed in simulation. We need to balance design and randomness in a way that generates reasonable networks with given characteristics and predictable variability. This paper presents such a method, Combined Optimization and Layered Design (COLD), incorporating randomness and design principles to create ensembles of PoP-level synthetic networks.

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Section: Resultsmentioning

confidence: 99%

“…It generates link capacities and distances along with routing. 6. The PoP-level model has only four parameters, and we show why at least this many are needed.…”

Section: Background and Comparisonsmentioning

confidence: 98%

Section: -Attributed To a Einsteinmentioning

confidence: 99%

Section: A Network's Form Is Driven By Real Costs and Technicalmentioning

confidence: 99%

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Cold

Bowden

Roughan

Bean

2014

Proceedings of the 10th ACM International on Conference on Emerging Networking Experiments and Technologies

Self Cite

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“…have developed both deterministic and stochastic models by using the Kronecker product of graphs to generate complex networks which inherit properties of real world networks. In [2], the authors had presented generalized graph products methodology to generate different types of complex networks. In this paper, we propose a model for complex networks by using the concept of corona product of graphs.…”

Section: Introductionmentioning

confidence: 99%

Structural and spectral properties of corona graphs

Sharma

Adhikari

Mishra

2017

Discrete Applied Mathematics

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Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two graphs, we define Corona graphs. Given a small simple connected graph which we call seed graph, Corona graphs are defined by taking corona product of a seed graph iteratively. We show that the cumulative degree distribution of Corona graphs decay exponentially when the seed graph is regular and cumulative betweenness distribution follows power law when seed graph is a clique. We determine explicit formulae of eigenvalues, Laplacian eigenvalues and signless Laplacian eigenvalues of Corona graphs when the seed graph is regular. Computable expressions of eigenvalues and signless Laplacian eigenvalues of Corona graphs are also obtained when the seed graph is a star graph.

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