All Questions
Tagged with random-graphs spectral-graph-theory
7 questions with no upvoted or accepted answers
2
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Expansion of random subgraphs of a bi-regular bipartite graph
Let $G = (L, R, E)$ be a bi-regular bipartite graph, with $|L|=n$ and $|R| = C \cdot n$, where $C$ is a large constant. Let $d$ be its (constant) right-degree.
We know $G$ is a good spectral expander. ...
- 225
1
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91
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Diameters of random bipartite graphs
Given two partite sets of vertices $U$ and $V$ of size $n$. Each vertex in $U$ uniformly randomly selects $K$ ($K$ is a constant and $K\ll n$) vertices in $V$ without replacement and connects a ...
- 11
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Controlling quantity related to Laplacian pseudo-inverse of Erdős–Rényi graph
Consider an $n$-node undirected graph $G = (V, E)$ equipped with weights $W$. Let $L$ be the weighted graph Laplacian matrix, i.e. $L_{ij} = -W_{(i,j)}$ for $(i,j)\in E$ and $L_{ii} = \sum_{j:(i,j)\in ...
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Angles between edges of a geometric graph and graph invariants
Are there any clever ways in which the angles between edges in a geometric graph are encoded in the graph spectrum, or another object associated with the graph?
I'm interested to see what else is ...
- 640
1
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61
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$\exp(-Cn^{\epsilon})$ estimate for probability of Brouwer-Haemers condition in Erdos-Renyi-like random graph
For any $n$-vertex graph $G$, we have the inequality $\lambda_i^{L_G}\geq D_i-i+2,$ where $L_G$ denotes the Laplacian of $G$ and $\lambda_i^{L_G}$ denotes the $i^\text{th}$ largest eigenvalue and $D_i$...
- 276
1
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209
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Characterization of k-walk-equivalent graphs
Let $G=(V,E)$ be an undirected graph. A walk of length $k$ in $G$ is a sequence of vertices $v_1,v_2,\ldots,v_{k+1}$ in $V$ such that $(v_i,v_{i+1})\in E$ for each $i=1,2,\ldots,k$.
Call two graphs $...
- 493
0
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101
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4-cycles vs eigenvalue information on quasi-random graphs
My (philosophical) question arises from reading the wonderful paper of Chung-Graham-Wilson where the authors introduces the notion of quasi-random graphs.
The main purpose of the paper is to show ...
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