Related papers: Random Processes with High Variance Produce Scale …

The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e.…

Generated networks are widely used in network-based research as a convenient simulation environment. Generating universal networks that more accurately reflect real-world patterns is a cornerstone task. This study proposes a vari-linear…

We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in the network in order to produce a scale-free graph with given exponent lambda for the degree distribution, but the…

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…

We are interested in the asymptotics of random trees built by linear preferential attachment, also known in the literature as Barab\'asi-Albert trees or plane-oriented recursive trees. We first prove a conjecture of Bubeck, Mossel \& R\'acz…

We study the statistical properties of the sampled scale-free networks, deeply related to the proper identification of various real-world networks. We exploit three methods of sampling and investigate the topological properties such as…

In this paper, we propose a growing random complex network model, which we call context dependent preferential attachment model (CDPAM), when the preference of a new node to get attached to old nodes is determined by the local and global…

Small-world architectures may be implicated in a range of phenomena from disease propagation to networks of neurons in the cerebral cortex. While most of the recent attention on small-world networks has focussed on the effect of introducing…

Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…

Many social networks exhibit assortative mixing so that the predictions of uncorrelated models might be inadequate. To analyze the role of assortativity we introduce an algorithm which changes correlations in a network and produces…

Continuous-time branching processes (CTBPs) are powerful tools in random graph theory, but are not appropriate to describe real-world networks, since they produce trees rather than (multi)graphs. In this paper we analyze collapsed branching…

Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach, Cygan, {\L}acki,…

In this paper, we propose a general model for collaboration networks. Depending on a single free parameter "{\bf preferential exponent}", this model interpolates between networks with a scale-free and an exponential degree distribution. The…

Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential…

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…

We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned…

A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…

Since network motifs are an important property of networks and some networks have the behaviors of rewiring or reducing or adding edges between old vertices before new vertices entering the networks, we construct our non-randomized model…

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…