Related papers: Random multi-hooking networks
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we…
Sampling random nodes is a fundamental algorithmic primitive in the analysis of massive networks, with many modern graph mining algorithms critically relying on it. We consider the task of generating a large collection of random nodes in…
We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…
This paper establishes a relation between scale-free networks and Markov chains, and proposes a computation framework for degree distributions of scale-free networks. We first find that, under the BA model, the degree evolution of…
We consider ad-hoc networks consisting of $n$ wireless nodes that are located on the plane. Any two given nodes are called neighbors if they are located within a certain distance (communication range) from one another. A given node can be…
This article discusses the properties of extremes of degree sequences calculated from network data. We introduce the notion of a normalized degree, in order to permit a comparison of degree sequences between networks with differing numbers…
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…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
In this paper we study a random graph with $N$ nodes, where node $j$ has degree $D_j$ and $\{D_j\}_{j=1}^N$ are i.i.d. with $\prob(D_j\leq x)=F(x)$. We assume that $1-F(x)\leq c x^{-\tau+1}$ for some $\tau>3$ and some constant $c>0$. This…
Great part of the interest in complex networks has been motivated by the presence of structured, frequently non-uniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they…
In this paper we consider a simple model of random graph process with {\it hard} copying as follows: At each time step $t$, with probability $0<\alpha\leq 1$ a new vertex $v_t$ is added and $m$ edges incident with $v_t$ are added in the…
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…
We investigate the joint distribution of nodes of small degrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the joint asymptotic distribution of the number of the nodes of outdegree $0$…
We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e.\ an existing vertex is copied and every edge leading to the copied vertex is copied with independent probability $p$. In addition,…
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…
Seeded PageRank is an important network analysis tool for identifying and studying regions nearby a given set of nodes, which are called seeds. The seeded PageRank vector is the stationary distribution of a random walk that randomly resets…
In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…
The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively and linking each to an earlier node of degree k with attachment probability A_k. When A_k grows slower…