Constructing and sampling graphs with a prescribed joint degree distribution

Stanton, Isabelle; Pınar, Ali

doi:10.1145/2133803.2330086

Cited by 59 publications

(92 citation statements)

References 64 publications

(65 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, in [9] and [76], algorithms are introduced for constructing and sampling simple graphs with a given joint degree matrix J. Unfortunately the algorithms apply to graphs of fixed size and no asymptotic results are yet known.…”

Section: Generating Graphs With Specific Degree-degree Correlationsmentioning

confidence: 99%

Asymptotic analysis of network structures: degree-degree correlations and directed paths

Hoorn

View full text Add to dashboard Cite

Opgedragen aan mijn neefje Wouter: Iter tibi prosperitate scientiaque obseratur et aetas amore sapientiaque plena sit. VoorwoordGeen enkele uitzonderlijke prestatie is het werk van slechts één persoon. En hoewel ik, met betrekking tot dit proefschrift, geen uitspraak zal doen over het eerste deel van dit statement, is het tweede deel absoluut waar. Ik wil dan ook graag iedereen bedanken die hieraan op een of andere manier heeft bijgedragen. Sommige mensen wil ik in het bijzonder noemen en daarvoor zal ik deze pagina's gebruiken. Toen ik, iets meer dan vier jaar geleden, in de zomer van 2012 besloot om een PhD te doen, was ik niet helemaal zeker van mij zaak, gezien het feit dat ik al een jaar geen wiskunde meer bedreven had. Voor mijn interview in Enschede was ik dan ook erg zenuwachtig. Helemaal omdat het hier zelfs over een onderwerp ging waar ik nog nooit iets mee gedaan had gedurende mijn tijd als student. Richard, dank je dat je mij deze kans hebt gegeven, voor je vertrouwen in mij als onderzoeker en het opnemen van mij in je groep. Ik zal altijd met veel plezier terugdenken aan mijn tijd in Twente.Voor mijn dagelijkse begeleiding kon ik terecht bij Nelly. Ik weet nog goed dat ze mij tijdens ons eerste overleg meteen vertelde dat ze hele hoge verwachtingen van me had. Ik kan alleen maar hopen dat ik daar ergens in de buurt van ben gekomen. Maar Nelly, jij bent mijn verwachtingen als begeleider meer dan overstegen. Het voelt ergens vreemd om dit in het Nederlands te schrijven. Ondanks het feit dat je deze taal goed beheerst communiceren wij namelijk altijd met elkaar in het Engels. De stewardess van de KLM begreep er in ieder geval niets van. Jij was altijd heel duidelijk in wat je van me verwachtte en had altijd een plan klaar, hoewel dit laatste vaak erg flexibel was. Je gaf me de vrijheid om mijn onderzoek in te richten en liet me vaak mijn gang gaan, waar je hulp bood als ik dat nodig had. Maar je was ook streng, direct en ondubbelzinnig op de momenten dat dit moest. Naast een meer dan uitstekende begeleider ben je een ook een hele goede vriendin van me geworden. Ik heb ontzettend genoten van de conferenties die wij samen hebben bezocht en alle avonturen die wij hebben beleefd. Ik hoop dan ook dat wij nog heel lang vrienden zullen blijven. Maar nu zal ik verder gaan, voordat je me weer vertelt dat ik als een meisje schrijf.Gedurende mijn PhD heb ik de mogelijkheid gehad om twee onderzoeksstages in het buitenland te doen en daar ben ik heel dankbaar voor.Mariana, thank you for inviting me to Columbia. It was my first time collaborating with someone other than my supervisor and I more than appreciated the opportunity you gave me. When writing this thesis, especially when dealing with some technical proofs, I realized how much I learned from you in only these vii Asymptotic analysis of network structures: degree-degree correlations and directed paths two weeks. I also want to thank you for being part of my defense committee and reading my thesis. I hope to continue our collaboration in the future and learn ...

show abstract

Section: Generating Graphs With Specific Degree-degree Correlationsmentioning

confidence: 99%

Asymptotic analysis of network structures: degree-degree correlations and directed paths

Hoorn

View full text Add to dashboard Cite

show abstract

“…This impacts the joint-degree distribution, the degree distribution of the neighbors of a vertex as a function of the degree of the vertex. The joint-degree distribution is shown to be correlated to other important graph metrics such as conductance [29]. Here, we measure how close to the original graph the generated joint-degree distribution is for Darwini, BTER and Kronecker.…”

Section: Btermentioning

confidence: 99%

Generating synthetic social graphs with Darwini

Edunov

Logothetis

Wang

et al. 2018

EasyChair Preprints

View full text Add to dashboard Cite

Abstract-Synthetic graph generators facilitate research in graph algorithms and graph processing systems by providing access to graphs that resemble real social networks while addressing privacy and security concerns. Nevertheless, their practical value lies in their ability to capture important metrics of real graphs, such as degree distribution and clustering properties. Graph generators must also be able to produce such graphs at the scale of real-world industry graphs, that is, hundreds of billions or trillions of edges.In this paper, we propose Darwini, a graph generator that captures a number of core characteristics of real graphs. Importantly, given a source graph, it can reproduce the degree distribution and, unlike existing approaches, the local clustering coefficient distribution. Furthermore, Darwini maintains a number of metrics, such as graph assortativity, eigenvalues, and others. Comparing Darwini with state-of-the-art generative models, we show that it can reproduce these characteristics more accurately. Finally, we provide an open source implementation of Darwini on the vertex-centric Apache Giraph TM model that can generate synthetic graphs with up to 3 trillion edges.

show abstract

“…Exponential Random Graph Models (ERGMs) [15] can theoretically model the degree distribution, clustering and assortativity, but their learning and sampling is (at best) quadratic in runtime. Sampling from the Joint Degree Distribution (JDD) model is quadratic over the number of nodes [16]. In contrast, the CL family of models (and our proposed extension) is subquadratic, making them scale to large data.…”

Section: Generative Models Of Graphsmentioning

confidence: 99%

“…Two existing models that produce networks with assortativity are the Block Two-Level Erdos-Renyi (BTER) graph model [5], and the Joint Degree Distribution (JDD) model [16]. The BTER model [5] groups vertices with similar degrees into blocks of vertices: vertices within the same block have higher probability of linking, while vertices across blocks have significantly lower probability.…”

Section: Introductionmentioning

confidence: 99%

“…This includes negative assortativity (i.e., high degree nodes link primarily to low degree nodes), which occurs in many real-world networks. The recent JDD model [16] estimates a joint distribution over the degrees of incident nodes, and since assortativity is simply a function of the joint degree distribution, JDD can model it. However, the JDD model does not have a scalable sampling method, since its mixing time is currently quadratic in the number of nodes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Assortativity in Chung Lu Random Graph Models

Mussmann

Moore

Pfeiffer

et al. 2014

Proceedings of the 8th Workshop on Social Network Mining and Analysis

View full text Add to dashboard Cite

Due to the widespread interest in networks as a representation to investigate the properties of complex systems, there has been a great deal of interest in generative models of graph structure that can capture the properties of networks observed in the real world. Recent models have focused primarily on accurate characterization of sparse networks with skewed degree distributions, short path lengths, and local clustering. While assortativity-degree correlation among linked nodes-is used as a measure to both describe and evaluate connectivity patterns in networks, there has been little effort to explicitly incorporate patterns of assortativity into model representations. This is because many graph models are edge-based (modeling whether a link should be placed between a pair of nodes i and j) and assortativity is a second-order characteristic that depends on the global properties of the graph (i.e., the final degree of i and j). As such, it is difficult to incorporate direct optimization of assortativity into edge-based generative models.One exception is the BTER method [5], which generates graphs with positive assortativity (e.g., high degree nodes link to each other). However, BTER does not directly estimate assortativity and also is not applicable for networks with negative assortativity (e.g, high degree nodes link primarily to low degree nodes). In this work, we present a novel approach to directly model observed assortativity (both positive and negative) via accept-reject sampling. Our key observation is to use a coarse approximation of the observed joint degree distribution and modify the likelihood that two nodes i, j should link based on the output properties of the original model. We implement our approach as an augmentation of Chung-Lu models and refer to it as Binning Chung Lu (BCL). We apply our method to six network datasets and show that it captures assortativity significantly more accurately than other methods while maintaining other graph properties of the original CL models. Also, our BCL approach is efficient (linear in the number of observed edges), thus it scales easily to large networks.

show abstract

Constructing and sampling graphs with a prescribed joint degree distribution

Cited by 59 publications

References 64 publications

Asymptotic analysis of network structures: degree-degree correlations and directed paths

Asymptotic analysis of network structures: degree-degree correlations and directed paths

Generating synthetic social graphs with Darwini

Assortativity in Chung Lu Random Graph Models

Contact Info

Product

Resources

About