Related papers: Correlations in random Apollonian network

Many complex networks demonstrate a phenomenon of striking degree correlations, i.e., a node tends to link to other nodes with similar (or dissimilar) degrees. From the perspective of degree correlations, this paper attempts to characterize…

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…

We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree…

We introduce a minimal model of small-world growing network generated by attaching to edges. The produced network is a plane graph which exists in real-life world. We obtain the analytic results of degree distribution decaying exponentially…

We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already…

In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…

Motivated by widely observed examples in nature, society and software, where groups of already related nodes arrive together and attach to an existing network, we consider network growth via sequential attachment of linked node groups, or…

While degree correlations are known to play a crucial role for spreading phenomena in networks, their impact on the propagation speed has hardly been understood. Here we investigate a tunable spreading model on scale-free networks and show…

Many networks contain correlations and often conventional analysis is incapable of incorporating this often essential feature. In arXiv:0708.2176, we introduced the link-space formalism for analysing degree-degree correlations in evolving…

In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree…

In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the…

In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree…

The Erd\H{o}s-R\'enyi random graph is the simplest model for node degree distribution, and it is one of the most widely studied. In this model, pairs of $n$ vertices are selected and connected uniformly at random with probability $p$,…

We perform an analytical analysis of the long-range degree correlation of the giant component in an uncorrelated random network by employing generating functions. By introducing a characteristic length, we find that a pair of nodes in the…

We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is…

A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node,…

We study parallel algorithms for correlation clustering. Each pair among $n$ objects is labeled as either "similar" or "dissimilar". The goal is to partition the objects into arbitrarily many clusters while minimizing the number of…

Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…

Based on the formation of triad junctions, the proposed mechanism generates networks that exhibit extended rather than single power law behavior. Triad formation guarantees strong neighborhood clustering and community-level characteristics…

We offer an example of an network model with a power law degree distribution, P(k) ~ k^{-alpha}, for nodes but which nevertheless has a well-defined geography and a nonzero threshold percolation probability for alpha>2, the range of…