On the mixed adjacency matrix of a mixed graph

Adiga, Chandrashekara; Rakshith, B. R.; So, Wasin

doi:10.1016/j.laa.2016.01.033

Cited by 25 publications

(12 citation statements)

References 5 publications

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“…Membership values Adjacency (u, v) μ (u, v) number (3,6) 0.32 0.32 (4,9) 0.22 0.22 (4,16) 0.04 0.04 (7,9) 0.22 0.22 (9,14) 0.1 0.1 link membership values is the minimum of end vertex membership values. The edge membership values…”

Section: Undirected Edgesmentioning

confidence: 99%

Fuzzy mixed graphs and its application to identification of COVID19 affected central regions in India

Das¹,

Naseem

Samanta³

et al. 2021

IFS

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In the recent phenomenon of social networks, both online and offline, two nodes may be connected, but they may not follow each other. Thus there are two separate links to be given to capture the notion. Directed links are given if the nodes follow each other, and undirected links represent the regular connections (without following). Thus, this network may have both types of relationships/ links simultaneously. This type of network can be represented by mixed graphs. But, uncertainties in following and connectedness exist in complex systems. To capture the uncertainties, fuzzy mixed graphs are introduced in this article. Some operations, completeness, and regularity and few other properties of fuzzy mixed graphs are explained. Representation of fuzzy mixed graphs as matrix and isomorphism theorems on fuzzy mixed graphs are developed. A network of COVID19 affected areas in India are assumed, and central regions are identified as per the proposed theory.

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Section: Undirected Edgesmentioning

confidence: 99%

Fuzzy mixed graphs and its application to identification of COVID19 affected central regions in India

Das¹,

Naseem

Samanta³

et al. 2021

IFS

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“…In the following, we will give two reduction formulas for P M (x), which are similar to those of adjacency matrices of simple graphs [11,Section 2] and those of Hermitian adjacency matrices of the first kind for mixed graphs [2]. Theorem 3.6.…”

Section: The Characteristic Polynomial Of Mixed Graphsmentioning

confidence: 99%

Hermitian adjacency matrix of the second kind for mixed graphs

Li¹,

Yu²

2021

Preprint

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This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind introduced by Mohar [21]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u to v is equal to the sixth root of unity ω = 1+i √ 3 2 (and its symmetric entry is ω = 1−i √ 32 ); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. The main results of this paper include the following: Some interesting properties are discovered about the characteristic polynomial of this novel matrix. Cospectral problems among mixed graphs, including mixed graphs and their underlying graphs, are studied. We give equivalent conditions for a mixed graph that shares the same spectrum of its Hermitian adjacency matrix of the second kind (H S -spectrum for short) with its underlying graph. A sharp upper bound on the H Sspectral radius is established and the corresponding extremal mixed graphs are identified. Operations which are called three-way switchings are discussed-they give rise to a large number of H S -cospectral mixed graphs. We extract all the mixed graphs whose rank of its Hermitian adjacency matrix of the second kind (H S -rank for short) is 2 (resp. 3). Furthermore, we show that all connected mixed graphs with H S -rank 2 can be determined by their H S -spectrum. However, this does not hold for all connected mixed graphs with H S -rank 3. We identify all mixed graphs whose eigenvalues of its Hermitian adjacency matrix of the second kind (H S -eigenvalues for short) lie in the range (−α, α) for α ∈ √ 2, √ 3, 2 .

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“…Liu and Li introduced Hermitian-adjacency matrices of mixed graphs. After that, Adiga et al [4] described the adjacency matrix of a mixed graph. In that paper, the matrix was defined as a real matrix.…”

Section: Introductionmentioning

confidence: 99%

A Study on Semi-directed Graphs for Social Media Networks

Samanta¹,

Pal²,

Mahapatra³

et al. 2021

IJCIS

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In the literature of graph theory, networks are represented as directed graphs or undirected graphs and a mixed of both combinations. In today's era of computing, networks like brain and facebook that do not belong to any of the mentioned networks category and in fact, it belongs to the combination of both networks which have connections as directed as well as undirected. To represent such networks, semi-directed graphs have been studied in this paper that provides the detailed mathematical fundamentals related to better understand the conceptualization for social media networks. This paper also discusses the suitable matrices analyze for the representation of the graphs. Few new terminologies like incidence number, complete-incidence related to semi-directed graphs and counter isomorphism of semi-directed graphs have been inculcated. A centrality measure, namely incidence centrality, has also been proposed based on incidence number on neighbors in social media networks.

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On the mixed adjacency matrix of a mixed graph

Cited by 25 publications

References 5 publications

Fuzzy mixed graphs and its application to identification of COVID19 affected central regions in India

Fuzzy mixed graphs and its application to identification of COVID19 affected central regions in India

Hermitian adjacency matrix of the second kind for mixed graphs

A Study on Semi-directed Graphs for Social Media Networks

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