Related papers: Simple evolving random graphs
In this article we consider several probabilistic processes defining random grapha. One of these processes appeared recently in connection with a factorization problem in the symmetric group. For each of the probabilistic processes, we…
The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…
Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…
Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Inspired by a concept in comparative genomics, we investigate properties of randomly chosen members of G_1(m,n,t), the set of bipartite graphs with $m$ left vertices, n right vertices, t edges, and each vertex of degree at least one. We…
We consider a time varying analogue of the Erd{\H o}s-R{\' e}nyi graph and study the topological variations of its associated clique complex. The dynamics of the graph are stationary and are determined by the edges, which evolve…
We study a random graph model which combines properties of the edge percolation model on Z^d and a classical random graph G(n,c/n). We show that this model, being a homogeneous random graph, has a natural relation to the so-called "rank 1…
We study "positive" graphs that have a nonnegative homomorphism number into every edge-weighted graph (where the edgeweights may be negative). We conjecture that all positive graphs can be obtained by taking two copies of an arbitrary…
We show that for any fixed dense graph G and bounded-degree tree T on the same number of vertices, a modest random perturbation of G will typically contain a copy of T . This combines the viewpoints of the well-studied problems of embedding…
We study an equilibrium statistical mechanical model of tree graphs which are made up of a linear subgraph (the spine) to which leaves are attached. We prove that the model has two phases, a generic phase where the spine becomes infinitely…
Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic…
We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…
A single permutation, seen as union of disjoint cycles, represents a regular graph of degree two. Consider $d$ many independent random permutations and superimpose their graph structures. It is a common model of a random regular (multi-)…
In their seminal paper introducing the theory of random graphs, Erd\H{o}s and R\'{e}nyi considered the evolution of the structure of a random subgraph of $K_n$ as the density increases from $0$ to $1$, identifying two key points in this…
Real networks are often dynamic. In response to it, analyses of algorithms on {\em dynamic networks} attract more and more attentions in network science and engineering. Random walks on dynamic graphs also have been investigated actively in…
Let P_{n,m} denote the graph taken uniformly at random from the set of all planar graphs on {1,2,..., n} with exactly m(n) edges. We use counting arguments to investigate the probability that P_{n,m} will contain given components and…
Random hypergraphs extend the classical notion of random graphs by allowing hyperedges to join more than two vertices, making them well-suited for modeling higher-order interactions in complex systems. Despite their broad applicability,…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
We study evolution algebras of arbitrary dimension. We analyze in deep the notions of evolution subalgebras, ideals and non-degeneracy and describe the ideals generated by one element and characterize the simple evolution algebras. We also…