Related papers: Logarithmic typical distances in preferential atta…
We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…
Log-Euclidean distances are commonly used to quantify the similarity between positive definite matrices using geometric considerations. This paper analyzes the behavior of this distance when it is used to measure closeness between…
Introduced by Mallows in statistical ranking theory, Mallows permutation model is a class of non-uniform probability measures on the symmetric group $S_n$ that depend on a distance metric $d(\sigma,\tau)$ on $S_n$ and a scale parameter…
Maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible distance from each other relative to any other…
Preferential attachment networks are a type of random network where new nodes are connected to existing ones at random, and are more likely to connect to those that already have many connections. We investigate further a family of models…
We study a new class of preferential attachment trees with \emph{self-reinforcement}. At each time, each vertex is assigned a weight equal to the cumulative sum over past times of an affine function of its degree. A new vertex attaches…
This paper relates parameter distance to gradient breakdown for a broad class of nonlinear compositional functions. The analysis leads to a new distance function called deep relative trust and a descent lemma for neural networks. Since the…
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…
We investigate a class of network growth rules that are based on a redirection algorithm wherein new nodes are added to a network by linking to a randomly chosen target node with some probability 1-r or linking to the parent node of the…
We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following…
We study preferential attachment (PA) trees with general attachment functions. PA suggests an intuitive monotonicity: if high-degree vertices are rewarded more strongly, then the resulting tree should become shallower. We examine this…
Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting…
We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses $r$ vertices…
We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either…
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…
In this paper asymptotic methods are used to form lower bounds on the free distance to constraint length ratio of several ensembles of regular, asymptotically good, protograph-based LDPC convolutional codes. In particular, we show that the…
The metric dimension of a graph $G$ is the minimal size of a subset $R$ of vertices of $G$ that, upon reporting their graph distance from a distingished (source) vertex $v^\star$, enable unique identification of the source vertex $v^\star$…
We propose a random graph model with preferential attachment rule and \emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random…
In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$…
We consider random walk and self-avoiding walk whose 1-step distribution is given by $D$, and oriented percolation whose bond-occupation probability is proportional to $D$. Suppose that $D(x)$ decays as $|x|^{-d-\alpha}$ with $\alpha>0$.…