5 problems

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Clustering conjecture for spatial multiclass wireless networks
Clustering conjecture. The spatial multiclass wireless network displays the same clustering behavior in the stationary regime.
Conjectureopenspatial-networks stochastic-processes wireless-networksarXiv posted 2 days ago
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Long edges in the scenario-B potential infection graph
Long-edge conjecture for scenario B. There exists $\phi>0$ such that, if $\lambda=n^{-\phi}$ , a.a.s. $I_n$ contains an edge of length greater than $\lambda$ .
Conjectureopenepidemic-spread random-graphs spatial-networksarXiv posted 2 days ago
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Long jumps between communities in scenario B
Scenario B long-jump conjecture. In scenario B, the infection will take long jumps between communities.
Conjectureopenepidemic-spread social-networks spatial-networksarXiv posted 2 days ago
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The logarithmic diameter conjecture for the SPA model giant component
Let $m=2$ and let $p,A1 in(0,1)$ be parameters of the SPA model, with $A2$ chosen sufficiently large. The giant component is the largest connected component of the graph produc…
Conjectureopengraph-diameter random-graphs spatial-networksarXiv posted 2 days ago
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The critical-threshold conjecture for robustness of spatial preferential attachment networks
Robustness threshold conjecture. Non-robustness occurs in any dimension if
Conjectureopenpercolation preferential-attachment spatial-networksarXiv posted 2 days ago

5 problems

Clustering conjecture for spatial multiclass wireless networks

Long edges in the scenario-B potential infection graph

Long jumps between communities in scenario B

The logarithmic diameter conjecture for the SPA model giant component

The critical-threshold conjecture for robustness of spatial preferential attachment networks