Add to ORKGAbstract. Complex real-world networks such as the web graph are often mod-elled as directed graphs evolving over time, where new vertices are joined to a constant m number of existing vertices of prescribed type. We consider a cer-tain on-line random construction of a countably infinite graph with out-degree m, and show that with probability 1 the construction gives rise to a unique isomorphism type. We show that random semi-directed graphs are prime mod-els in a certain first-order theory. We study algebraic properties of random semi-directed graphs; in particular, we prove that their automorphism groups embed all countable groups. 1
AbstractHodges et al. showed that the countable random graph has the small index property. The stron...
Hodges et al. showed that the countable random graph has the small index property. The stronger resu...
Given a graph G, the modularity of a partition of the vertex set measures the extent to which edge d...
Motivated by models for real-world networks such as the web graph, we consider digraphs formed by ad...
The theory of random graphs, that is graphs generated by some prescribed random process, gained popu...
The study of random graphs has traditionally been dominated by the closely-related models G(n, m), i...
Much recent attention has focused on the study of models of massive real-world networks like the web...
We establish links between countable algebraically closed graphs and the endomorphisms of the counta...
Abstract. For a positive integer n, we introduce the new graph class of n-ordered graphs, which gene...
Abstract. The random ordered graph is the up to isomorphism unique countable homoge-neous linearly o...
AbstractFor a class of countably infinite ultrahomogeneous structures that generalize edge-colored g...
We classify isomorphism-invariant random digraphs \linebreak (IIRDs) according to where randomness l...
Abstract. We answer a question of P. Cameron’s by giving ex-amples of 2ℵ0 many non-isomorphic acycli...
We study the thresholds for the emergence of various properties in random subgraphs of (N,<). In par...
Abstract. Recently proposed models of self-organizing networks like the web graph often incorporate ...
AbstractHodges et al. showed that the countable random graph has the small index property. The stron...
Hodges et al. showed that the countable random graph has the small index property. The stronger resu...
Given a graph G, the modularity of a partition of the vertex set measures the extent to which edge d...
Motivated by models for real-world networks such as the web graph, we consider digraphs formed by ad...
The theory of random graphs, that is graphs generated by some prescribed random process, gained popu...
The study of random graphs has traditionally been dominated by the closely-related models G(n, m), i...
Much recent attention has focused on the study of models of massive real-world networks like the web...
We establish links between countable algebraically closed graphs and the endomorphisms of the counta...
Abstract. For a positive integer n, we introduce the new graph class of n-ordered graphs, which gene...
Abstract. The random ordered graph is the up to isomorphism unique countable homoge-neous linearly o...
AbstractFor a class of countably infinite ultrahomogeneous structures that generalize edge-colored g...
We classify isomorphism-invariant random digraphs \linebreak (IIRDs) according to where randomness l...
Abstract. We answer a question of P. Cameron’s by giving ex-amples of 2ℵ0 many non-isomorphic acycli...
We study the thresholds for the emergence of various properties in random subgraphs of (N,<). In par...
Abstract. Recently proposed models of self-organizing networks like the web graph often incorporate ...
AbstractHodges et al. showed that the countable random graph has the small index property. The stron...
Hodges et al. showed that the countable random graph has the small index property. The stronger resu...
Given a graph G, the modularity of a partition of the vertex set measures the extent to which edge d...