Questions tagged [network-theory]
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11
questions with no upvoted or accepted answers
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Transversal deviation in first passage percolation
Take the lattice $\mathbb{L}^{2}=(\mathbb{Z}^{2},\mathbb{E}^{2})$ with i.i.d. $\text{U}[0,1]$ weights on the edges, and the random variable $D$ giving the maximal transversal deviation of the geodesic ...
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45
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Bounds on the spectral radius of a perturbed directed graph
Suppose $(G_n)$ is a sequence of strongly connected directed graphs (without multiple edges) with $G_n$ having $n$ edges such that the adjacency matrix $A_n$ of $G_n$ is primitive, and let $(G_n’)$ be ...
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31
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Both-way flows in a directed graph
Let $G$ be a finite directed graph, and let $s,t$ be two distinct vertices.
Problem $1(s,t)$. Find the maximum number of mutually edge-disjoint directed paths from $s$ to $t$. OK, I didn't think of ...
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48
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Is a function of a centrality measure a centrality measure?
I have been trying to wrap my head around the following question. Suppose you a have a centrality measure for a weighted, undirected network. Let's call the calculated centralities with $\pmb{x}>0$....
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69
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Is there a theory for forcing "sludge" through a network, analogous to electric current flows?
I'm familiar with the correspondence between reversible Markov chains, random walks, and electric current flows, as described in Probability on Trees and Networks by Lyons and Peres.
Is there an ...
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255
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total unimodularity of a matrix
Let G be the node-arc incidence matrix of a given directed network (rows of $G$ correspond to nodes and its columns correspond to arcs). Let $B_1,\dots, B_K$ denote a partition of the nodes of the ...
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30
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Number and different kinds of spnning trees in a weighted graph
We know that for a unweighted graph the number $\tau(\mathcal{G})$ of unique spanning trees of $\mathcal{G}$ is $$\tau(\mathcal{G})=\det L_\mathcal{G}^{\{n-1\}},$$ where $L_\mathcal{G}^{\{n-1\}}$ is ...
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58
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On the defect of a flow network
This problem in graph theory was actually motivated by some problems in Theory of Fractals.
To formulate the problem I need to recall some definitions related to flow network.
A flow network is a ...
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71
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An $n$-dimensional generalized Hoffman’s circulation theorem?
For a directed graph $G$, a 1-dimensional circulation is a function $f:E(G)\rightarrow \mathbb{R}$ such that for every $v\in V(G)$,
$$\sum_{uv\in E(G)}f(uv)=\sum_{vw\in E(G)}f(vw),$$
where $uv$ is an ...
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40
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Properties of preferential attachment such as spectral gap
Short question:
Is there a good math reference on the properties of preferential attachment graphs? In particular, expansion properties seem to interest me.
More details:
I try to investigate the ...
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Does the Lawrence–Krammer representation provide a quantized action on the space of networks?
Let $\rho:B_n \rightarrow H_2(\overline{C_2 P_n})$ denote the Lawrence–Krammer representation of the braid group on $n$ symbols. The group $H_2(\overline{C_2 P_n})$ is a free $\mathbb{Z}[q,t]$-module ...