Generating connected random graphs

Gray, Caitlin; Mitchell, Lewis; Roughan, Matthew

doi:10.1093/comnet/cnz011

Cited by 7 publications

(4 citation statements)

References 32 publications

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“…Nevertheless, one observes some interesting differences in comparison to the HMF results. To some extent these differences are due, in the scale-free case, to the real random occurrence of large hubs in the network, while in the HMF approximation all hubs contribute "virtually" to dynamics, each one with a small probability [22][23][24][25].…”

Section: Numerical Solutions Of the Bass Diffusion Equation On Assort...mentioning

confidence: 99%

Generation of Scale-Free Assortative Networks via Newman Rewiring for Simulation of Diffusion Phenomena

Di Lucchio,

Modanese

2024

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By collecting and expanding several numerical recipes developed in previous work, we implement an object-oriented Python code, based on the networkX library, for the realization of the configuration model and Newman rewiring. The software can be applied to any kind of network and “target” correlations, but it is tested with focus on scale-free networks and assortative correlations. In order to generate the degree sequence we use the method of “random hubs”, which gives networks with minimal fluctuations. For the assortative rewiring we use the simple Vazquez-Weigt matrix as a test in the case of random networks; since it does not appear to be effective in the case of scale-free networks, we subsequently turn to another recipe which generates matrices with decreasing off-diagonal elements. The rewiring procedure is also important at the theoretical level, in order to test which types of statistically acceptable correlations can actually be realized in concrete networks. From the point of view of applications, its main use is in the construction of correlated networks for the solution of dynamical or diffusion processes through an analysis of the evolution of single nodes, i.e., beyond the Heterogeneous Mean Field approximation. As an example, we report on an application to the Bass diffusion model, with calculations of the time tmax of the diffusion peak. The same networks can additionally be exported in environments for agent-based simulations like NetLogo.

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Section: Numerical Solutions Of the Bass Diffusion Equation On Assort...mentioning

confidence: 99%

Generation of Scale-Free Assortative Networks via Newman Rewiring for Simulation of Diffusion Phenomena

Di Lucchio,

Modanese

2024

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“…A more subtle sampling technique, for example applying the Metropolis-Hastings algorithm, could extend the results of this work substantially. [12] Table 5. For each n from 20 to 87, the probability that a graph chosen uniformly at random from the set of graphs with n vertices is universally solvable, approximated by 1,000,000 trials; all graphs chosen were incidentally connected.…”

Section: Future Workmentioning

confidence: 99%

Lights Out On A Random Graph

Forrest¹,

Nicole²

2021

Preprint

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We consider the generalized game Lights Out played on a graph and investigate the following question: for a given positive integer n, what is the probability that a graph chosen uniformly at random from the set of graphs with n vertices yields a universally solvable game of Lights Out? When n ≤ 11, we compute this probability exactly by determining if the game is universally solvable for each graph with n vertices. We approximate this probability for each positive integer n with n ≤ 87 by applying a Monte Carlo method using 1,000,000 trials. We also perform the analogous computations for connected graphs.

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“…A common proposal used when implementing MCMC on networks is to change a random node pair (i.e. creating a new edge or removing old edges) [7,19]. However, in sparse graphs non-edges are proposed much more often than edges, and the sampler wastes time proposing new edges that are likely to be rejected.…”

Section: Bayesian Inferencementioning

confidence: 99%

Bayesian Inference of Network Structure From Information Cascades

Gray

Mitchell

Roughan

2020

IEEE Trans. on Signal and Inf. Process. over Networks

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Contagion processes are strongly linked to the network structures on which they propagate, and learning these structures is essential for understanding and intervention on complex network processes such as epidemics and (mis)information propagation. However, using contagion data to infer network structure is a challenging inverse problem. In particular, it is imperative to have appropriate measures of uncertainty in network structure estimates, however these are largely ignored in most machine-learning approaches. We present a probabilistic framework that uses samples from the distribution of networks that are compatible with the dynamics observed to produce network and uncertainty estimates. We demonstrate the method using the well known independent cascade model to sample from the distribution of networks P(G) conditioned on the observation of a set of infections C. We evaluate the accuracy of the method by using the marginal probabilities of each edge in the distribution, and show the benefits of quantifying uncertainty to improve estimates and understanding, particularly with small amounts of data.

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Generating connected random graphs

Cited by 7 publications

References 32 publications

Generation of Scale-Free Assortative Networks via Newman Rewiring for Simulation of Diffusion Phenomena

Generation of Scale-Free Assortative Networks via Newman Rewiring for Simulation of Diffusion Phenomena

Lights Out On A Random Graph

Bayesian Inference of Network Structure From Information Cascades

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