Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information

Garrod, Matthew; Jones, Nick

doi:10.1103/physreve.98.052316

Cited by 2 publications

(2 citation statements)

References 53 publications

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“…In the continuous case, connection probability information has been used to forecast dynamics on spatial networks via diffusion [72,73] or PDE based approaches [39,74]. Given a node distribution and connectivity kernel, the predictability of dynamical properties in spatial networks is impacted by dimensionality and inhomogeneity in the node distribution [75]. We expect our ability to influence dynamics on spatial networks to depend on the same factors.…”

Section: Discussionmentioning

confidence: 99%

Influencing dynamics on social networks without knowledge of network microstructure

Garrod

Jones

2021

J. R. Soc. Interface.

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Social network-based information campaigns can be used for promoting beneficial health behaviours and mitigating polarization (e.g. regarding climate change or vaccines). Network-based intervention strategies typically rely on full knowledge of network structure. It is largely not possible or desirable to obtain population-level social network data due to availability and privacy issues. It is easier to obtain information about individuals’ attributes (e.g. age, income), which are jointly informative of an individual’s opinions and their social network position. We investigate strategies for influencing the system state in a statistical mechanics based model of opinion formation. Using synthetic and data-based examples we illustrate the advantages of implementing coarse-grained influence strategies on Ising models with modular structure in the presence of external fields. Our work provides a scalable methodology for influencing Ising systems on large graphs and the first exploration of the Ising influence problem in the presence of ambient (social) fields. By exploiting the observation that strong ambient fields can simplify control of networked dynamics, our findings open the possibility of efficiently computing and implementing public information campaigns using insights from social network theory without costly or invasive levels of data collection.

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Section: Discussionmentioning

confidence: 99%

Influencing dynamics on social networks without knowledge of network microstructure

Garrod

Jones

2021

J. R. Soc. Interface.

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“…We remark that this formalism extends to a multivariate Gaussian node distribution through an affine transformation of the node space V and scale matrix R (see Appendix G 3). This is what we refer to as the Gaussian random geometric graph (Gaussian RGG) [77]. (Arguably, this should be termed a doubly Gaussian RGG, where both the node distribution and connectivity kernel are Gaussian.)…”

Section: Gaussian Random Geometric Graphmentioning

confidence: 99%

Geodesic statistics for random network families

Loomba¹,

Jones²

2021

Preprint

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A key task in the study of networked systems is to derive local and global properties that impact connectivity, synchronizability, and robustness. Computing shortest paths or geodesics in the network yields measures of node centrality and network connectivity that can contribute to explain such phenomena. We derive an analytic distribution of shortest path lengths, on the giant component in the supercritical regime or on small components in the subcritical regime, of any sparse (possibly directed) graph with conditionally independent edges, in the infinite-size limit. We provide specific results for widely used network families like stochastic block models, dot-product graphs, random geometric graphs, and graphons. The survival function of the shortest path length distribution possesses a simple closed-form lower bound which is asymptotically tight for finite lengths, has a natural interpretation of traversing independent geodesics in the network, and delivers novel insight in the above network families. Notably, the shortest path length distribution allows us to derive, for the network families above, important graph properties like the bond percolation threshold, size of the giant component, average shortest path length, and closeness and betweenness centralities. We also provide a corroborative analysis of a set of 20 empirical networks. This unifying framework demonstrates how geodesic statistics for a rich family of random graphs can be computed cheaply without having access to true or simulated networks, especially when they are sparse but prohibitively large.

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Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information

Cited by 2 publications

References 53 publications

Influencing dynamics on social networks without knowledge of network microstructure

Influencing dynamics on social networks without knowledge of network microstructure

Geodesic statistics for random network families

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