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On two Laplacian matrices for skew gain graphs [PDF]

Electronic Journal of Graph Theory and Applications, 2021
Gain graphs are graphs where the edges are given some orientation and labeled with the elements (called gains) from a group so that gains are inverted when we reverse the direction of the edges.
Roshni T. Roy, Shahul Hameed K., Germina K.A.   +2 more
doaj   +2 more sources

On the adjacency matrix of a complex unit gain graph [PDF]

Linear and multilinear algebra, 2020
A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge.
Ranjit Mehatari, M. Rajesh Kannan, Aniruddha Samanta   +2 more
openalex   +3 more sources

Normalized Laplacians for gain graphs [PDF]

The American Journal of Combinatorics, 2022
We propose the notion of normalized Laplacian matrix \(\mathcal{L}(\Phi)\) for a gain graph \(\Phi\) and study its properties in detail, providing insights and counterexamples along the way. We establish bounds for the eigenvalues of \(\mathcal{L}(\Phi)\
M. Rajesh Kannan, Navish Kumar, Shivaramakrishna Pragada   +2 more
doaj   +4 more sources

Balancedness and the Least Laplacian Eigenvalue of Some Complex Unit Gain Graphs

Discussiones Mathematicae Graph Theory, 2020
Let 𝕋4 = {±1, ±i} be the subgroup of 4-th roots of unity inside 𝕋, the multiplicative group of complex units. A complex unit gain graph Φ is a simple graph Γ = (V (Γ) = {v1, . . .
Belardo Francesco, Brunetti Maurizio, Reff Nathan   +2 more
doaj   +2 more sources

Relation between the row left rank of a quaternion unit gain graph and the rank of its underlying graph

The Electronic Journal of Linear Algebra, 2023
Let $\Phi=(G,U(\mathbb{Q}),\varphi)$ be a quaternion unit gain graph (or $U(\mathbb{Q})$-gain graph), where $G$ is the underlying graph of $\Phi$, $U(\mathbb{Q})=\{z\in \mathbb{Q}: |z|=1\}$ is the circle group, and $\varphi:\overrightarrow{E}\rightarrow ...
Qiannan Zhou, Yong Lu
openalex   +3 more sources

Gain and Pain in Graph Partitioning: Finding Accurate Communities in Complex Networks [PDF]

Algorithms
This paper presents an approach to community detection in complex networks by simultaneously incorporating a connectivity-based metric and Max-Min Modularity.
Arman Ferdowsi, Maryam Dehghan Chenary
doaj   +2 more sources

NEPS of complex unit gain graphs

The Electronic Journal of Linear Algebra, 2023
A complex unit gain graph (or $\mathbb T$-gain graph) is a gain graph with gains in $\mathbb T$, the multiplicative group of complex units. Extending a classical construction for simple graphs due to Cvektovic, suitably defined noncomplete extended $p ...
Francesco Belardo, Maurizio Brunetti, Suliman Khan   +2 more
openalex   +3 more sources

The rank of a complex unit gain graph in terms of the matching number [PDF]

Linear Algebra and its Applications, 2019
Shengjie He, Rong‐Xia Hao, Fengming Dong   +2 more
openalex   +3 more sources

Information Gain Propagation: a new way to Graph Active Learning with Soft Labels [PDF]

International Conference on Learning Representations, 2022
Graph Neural Networks (GNNs) have achieved great success in various tasks, but their performance highly relies on a large number of labeled nodes, which typically requires considerable human effort.
Wentao Zhang, Yexin Wang, Zhenbang You, Meng Cao, Ping-Chia Huang, Jiulong Shan, Zhi Yang, Bin Cui   +7 more
semanticscholar   +1 more source

Rethinking the Expressive Power of GNNs via Graph Biconnectivity [PDF]

International Conference on Learning Representations, 2023
Designing expressive Graph Neural Networks (GNNs) is a central topic in learning graph-structured data. While numerous approaches have been proposed to improve GNNs in terms of the Weisfeiler-Lehman (WL) test, generally there is still a lack of deep ...
Bohang Zhang, Shengjie Luo, Liwei Wang, Di He   +3 more
semanticscholar   +1 more source