Related papers: Random multi-hooking networks
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
We consider two types of random networks grown in blocks. Hooking networks are grown from a set of graphs as blocks, each with a labelled vertex called a hook. At each step in the growth of the network, a vertex called a latch is chosen…
We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the…
We investigate a variety of statistical properties associated with the number of distinct degrees that exist in a typical network for various classes of networks. For a single realization of a network with N nodes that is drawn from an…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We introduce a new class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the ancestor of the target with probability r,…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…
We investigate to what extent the degree sequence of a directed network constrains the number of driver nodes. We develop a pair of algorithms that take a directed degree sequence as input and aim to output a network with the maximum or…
We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…