Questions tagged [complex-networks]
The complex-networks tag has no usage guidance.
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Real world applications of graph limits
It is well known that the area of graph limits (initiated by Lovász and coauthors) had provided a very powerful framework to deal with problems arising, for instance, in extremal combinatorics and ...
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What are the right mathematical tools / language to analyse complex networks over time?
In this article about human physiology as a complex network the authors say that:
"Lacking adequate analytic tools and a theoretical framework to probe
interactions within and among diverse ...
3
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Derivation of a series expansion
I am trying to derive the critical coupling strength for synchronisation in a network of phase oscillators with noisy input.
I am following the steps outlined in
Sakaguchi, Hidetsugu. "...
2
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1
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Random subgraph properties
Consider a graph $G$ of $N$ vertices and $M$ edges, and assume $G$ has typical complex network properties: it is not necessarily connected, but it has a high clustering coefficient and a giant ...
2
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Adjacency definition for a directed graph
For an undirected graph, we know that nodes are adjacent to each other if there is a link that connects them. What about adjacency for directed graphs? Is it based on:
outgoing links: node $n$ is ...
2
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2
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Which infinite random graphs with percolation threshold $p_c=0$ are transient?
I am interested in long-range percolation models with heavy-tailed degree distributions such as DHH13, GLM21, Y6. The simplest example is scale-free percolation in which vertices are elements $\mathbb{...
2
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what is the computational complexity of Louvain algorithm?
I am not able to find out the computational complexity of the Louvain Algorithm. Can anyone here help me? link of the paper given below:
DOI: 10.1088/1742-5468/2008/10/P10008
https://doi.org/10.1038/...
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How much algebra is preferable for studying/doing research in dynamical/complex system and networks
I asked this question earlier on Mathematics StackExchange (link), but I think it might be better to put it here.
This question seems quite broad to ask...
The situation here is that I'm a second-...
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The topological complexity of polytopes
Polytopes arise naturally when modelling fundamental structures in Biology such as RNA and proteins [1,2]. Recently, it occurred to me that a complexity measure on the topology of polytopes might be ...
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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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Research-level blogs on complex networks:
I'm an applied mathematician that has a research interest in complex networks for modelling biological systems and I wondered whether the MathOverflow community might know of research-level blogs that ...
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Do finite components get smaller as supercritical random graphs with an arbitrary degree sequence get denser?
I asked this question a few weeks ago on MSE but did not receive any responses so I am going to ask a related but more specific question here.
First some notation.
Let $\mathbb{G} = \mathbb{G}(n,\...