Consecutive One’s Properties for Matrices and Graphs Including Variable Diagonal Entries

Cozzens, Margaret B.; Mahadev, N. V. R.

doi:10.1007/978-1-4684-6381-1_3

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…. (4) Note that P remains a stochastic and irreducible matrix. Hence, the existence of A (and hence D , G ) is equivalent to the time-reversibility of the random walk governed by P (cf [14]).…”

Section: Type III Perturbationsmentioning

confidence: 99%

“…However, the node/edge connectivity only partly reflects the ability of graphs to retain connectedness after deletion. Other improved measures include super connectivity [1], fault diameter [13], scattering number [12], tenacity [4], expansion parameter [15], etc. In contrast to node/edge connectivity, these measures treat both the cost to damage a network and how badly the network is damaged.…”

Section: Introductionmentioning

confidence: 99%

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Perturbation results for the Estrada index in weighted networks

Shang¹

2011

J. Phys. A: Math. Theor.

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The logarithm of the Estrada index has been proposed recently as a spectral measure to character efficiently the robustness of complex networks. In this paper, we explore the Estrada index in weighted networks and develop various perturbation results based on spectral graph theory. It is shown that the robustness of a network may be enhanced even when some edge weights are reduced. This is of particular theoretical and practical significance to network design and optimization.

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Section: Type III Perturbationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Perturbation results for the Estrada index in weighted networks

Shang¹

2011

J. Phys. A: Math. Theor.

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“…This property is very useful in a variety of applications. See [28] for a discussion. An ordering of maximal cliques for which the maximal clique-vertex incidence matrix has 1's appearing consecutively in each column is called a consecutive ordering.…”

Section: What Graphs Are Interval Graphs?mentioning

confidence: 99%

Some Applications of Graph Theory

Roberts¹

2001

Combinatorial and Computational Mathematics

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We review three graph-theoretical concepts: graph coloring, intersection graph, and competition graph. For each, we mention a variety of applications, discuss generalizations of the concept arising from the applications, and describe some recent results and open questions. * Fred Roberts thanks the National Science Foundation for its support under grant NSF-SBR-9709134 to Rutgers University. He thanks the Combinatorial and Computational Mathematics Center at Pohang University of Science and Technology for sponsoring the conference that led to this paper and offers his congratulations and best wishes for Com 2 Mac's success.

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Applications of Combinatorics and Graph Theory to the Biological and Social Sciences: Seven Fundamental Ideas

Roberts

1989

Applications of Combinatorics and Graph Theory to the Biological and Social Sciences

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Consecutive One’s Properties for Matrices and Graphs Including Variable Diagonal Entries

Cited by 3 publications

References 19 publications

Perturbation results for the Estrada index in weighted networks

Perturbation results for the Estrada index in weighted networks

Some Applications of Graph Theory

Applications of Combinatorics and Graph Theory to the Biological and Social Sciences: Seven Fundamental Ideas

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