# Tagged Questions

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### Extensions of Matrix-Tree Theorem

It is known that for a given connected graph $G$ with $n$ labeled vertices, let $λ_1, λ_2, ..., λ_{n−1}$ be the non-zero eigenvalues of its Laplacian matrix. Then the number of spanning trees of $G$ ...
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### Adjacent matrix of undirected graph with a giant component

Assuming there is a undirected random graph $G=(V,E)$, $|V|=N$ and its adjacent matirx is $A$. What is the sufficient and necessary conditions of A for that there is a giant component of graph $G$? ...
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### Reachability in graphs using adjacent matrix

Assuming a graph $G$ with $N$ nodes distributed in a $\mathcal{L}\times\mathcal{L}$ area randomly. There is an edge between two nodes if and only if the Euler distance between them is equal or less ...
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### adjacency matrix of random geometric graphs [closed]

Consider a graph with N nodes. All nodes are distributed as a Poisson point process with density of λ in a L*L area. There is an edge between two nodes if and only if the distance between them is less ...