Relations between graphs and integer-pair sequences

Patrinos, A. N.; Hakimi, S. L.

doi:10.1016/0012-365x(76)90048-0

Cited by 31 publications

(18 citation statements)

References 3 publications

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“…The following characterization for a vector m with integer entries to be a graphical JDV is proved by Patrinos and Hakimi [12], Stanton and Pinar [15], and Czabarka et al [6]. As it provides simple necesssary and sufficient conditions for a vector to be realized as a graphical JDV, we call the result an Erdös-Gallai type theorem.…”

Section: Joint Degree Vectorsmentioning

confidence: 93%

On the Number of Non-Zero Elements of Joint Degree Vectors

Czabarka

Rauh

Sadeghi

et al. 2017

Electron. J. Combin.

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Joint degree vectors give the number of edges between vertices of degree i and degree j for 1 ≤ i ≤ j ≤ n − 1 in an n-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree vector as a function of n. This provides an upper bound on the number of estimable parameters in the exponential random graph model with bidegree-distribution as its sufficient statistics.

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Section: Joint Degree Vectorsmentioning

confidence: 93%

On the Number of Non-Zero Elements of Joint Degree Vectors

Czabarka

Rauh

Sadeghi

et al. 2017

Electron. J. Combin.

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“…Patrinos and Hakimi [46] introduced the integer-pair sequence of a graph, where each pair of an integer-pair sequence corresponds to an edge of the graph and contains the degrees of its end-vertices. They also gave necessary and sufficient conditions for the realizability of an integer-pair sequence.…”

Section: Degree-based Graph Invariantsmentioning

confidence: 99%

Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

Nishimura

Subramanya

2017

Combinatorial Optimization and Applications

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“…The general trends are in growing multiplex network models generally based on preferential attachment [17], [18], [19], [20], [21], simple statistic models [22], [23], [24], [25], [26], and ensembles of multilayered networks [27], [28], [29], [30] such as multilayered exponential random graphs [31]. In the current work, we focus on multiple layers as well as meso-scale properties like core-periphery and community structure.…”

Section: Related Workmentioning

confidence: 99%

A Generative Model for the Layers of Terrorist Networks

Adeniji

Cohick

Gera

et al. 2017

Proceedings of the 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2017

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Abstract-Data about terrorist networks is sparse and not consistently tagged as desired for research. Moreover, such data collections are hard to come across, which makes it challenging to propose solutions for the dynamic phenomenon driving these networks. This creates the need for generative network models based on the existing data.Dark networks show different characteristics than the other scale-free real world networks, in order to maintain the covert nature while remaining functional. In this work, we present the analysis of the layers of three terrorist multilayered networks. Based on our analysis, we categorize these layers into two types: evolving and mature. We propose generative models to create synthetic dark layers of both types. The proposed models are validated using the available datasets and results show that they can be used to generate synthetic layers having properties similar to the original networks' layers.

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Relations between graphs and integer-pair sequences

Cited by 31 publications

References 3 publications

On the Number of Non-Zero Elements of Joint Degree Vectors

On the Number of Non-Zero Elements of Joint Degree Vectors

Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

A Generative Model for the Layers of Terrorist Networks

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