scholarly journals A random graph of moderate density

2022 ◽  
Vol 27 (none) ◽  
Author(s):  
Ágnes Backhausz ◽  
Tamás F. Móri
Keyword(s):  
Random Graph ◽  
Moderate Density

Random graphs

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Large Scale ◽  
Random Network ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Random Graph Model ◽  
Definition Of ◽  
Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

scholarly journals A Note on the Majority Dynamics in Inhomogeneous Random Graphs

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Random Graph ◽  
Initial State ◽  
Time Step ◽  
Dynamic Monopoly ◽  
Inhomogeneous Random Graphs ◽  
Assignment Probability ◽  
Edge Probability ◽  
Consensus Reaching Process ◽  
Consensus Reaching ◽  
Inhomogeneous Random Graph

AbstractIn this note, we study discrete time majority dynamics over an inhomogeneous random graph G obtained by including each edge e in the complete graph $$K_n$$ K n independently with probability $$p_n(e)$$ p n ( e ) . Each vertex is independently assigned an initial state $$+1$$ + 1 (with probability $$p_+$$ p + ) or $$-1$$ - 1 (with probability $$1-p_+$$ 1 - p + ), updated at each time step following the majority of its neighbors’ states. Under some regularity and density conditions of the edge probability sequence, if $$p_+$$ p + is smaller than a threshold, then G will display a unanimous state $$-1$$ - 1 asymptotically almost surely, meaning that the probability of reaching consensus tends to one as $$n\rightarrow \infty $$ n → ∞ . The consensus reaching process has a clear difference in terms of the initial state assignment probability: In a dense random graph $$p_+$$ p + can be near a half, while in a sparse random graph $$p_+$$ p + has to be vanishing. The size of a dynamic monopoly in G is also discussed.

Soil fungal networks moderate density‐dependent survival and growth of seedlings

2021 ◽  
Author(s):  
Minxia Liang ◽  
Liuqing Shi ◽  
David F. R. P. Burslem ◽  
David Johnson ◽  
Miao Fang ◽  
...  
Keyword(s):  
Density Dependent ◽  
Moderate Density ◽  
Survival And Growth ◽  
Growth Of Seedlings

scholarly journals Very fast construction of bounded‐degree spanning graphs via the semi‐random graph process

2020 ◽  
Vol 57 (4) ◽  
pp. 892-919
Author(s):  
Omri Ben‐Eliezer ◽  
Lior Gishboliner ◽  
Dan Hefetz ◽  
Michael Krivelevich
Keyword(s):  
Random Graph ◽  
Bounded Degree
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