Related papers: Ranking algorithms on directed configuration netwo…
We introduce a new type of graphical model called a "cumulative distribution network" (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about…
We build up a directed network tracing links from a given integer to its divisors and analyze the properties of the Google matrix of this network. The PageRank vector of this matrix is computed numerically and it is shown that its…
In this paper some results about the controllability of spectral centrality in a complex network are presented. In particular, the inverse problem of designing an unweigthed graph with a prescribed centrality is considered, by showing that…
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…
Link directions are essential to the functionality of networks and their prediction is helpful towards a better knowledge of directed networks from incomplete real-world data. We study the problem of predicting the directions of some links…
We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…
After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with…
In the new field of financial systemic risk, the network of interbank counterparty relationships can be described as a directed random graph. In "cascade models" of systemic risk, this "skeleton" acts as the medium through which financial…
We propose a new measure to quantify the impact of a node $i$ in controlling a directed network. This measure, called `control contribution' $\mathcal{C}_{i}$, combines the probability for node $i$ to appear in a set of driver nodes and the…
We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank…
We present a comprehensive analysis of algebraic methods for controlling the stationary distribution of PageRank-like random walkers. Building upon existing literature, we compile and extend results regarding both structural control…
We consider a random model for directed graphs whereby an arc is placed from one vertex to another with a prescribed probability which may vary from arc to arc. Using perturbation bounds as well as Chernoff inequalities, we show that the…
The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…
We present a physics-inspired method for inferring dynamic rankings in directed temporal networks - networks in which each directed and timestamped edge reflects the outcome and timing of a pairwise interaction. The inferred ranking of each…
Let $d$ be a fixed large integer. For any $n$ larger than $d$, let $A_n$ be the adjacency matrix of the random directed $d$-regular graph on $n$ vertices, with the uniform distribution. We show that $A_n$ has rank at least $n-1$ with…
Ranking is one of the most fundamental problems in machine learning with applications in many branches of computer science such as: information retrieval systems, recommendation systems, machine translation and computational biology.…
The inference of rankings plays a central role in the theory of social choice, which seeks to establish preferences from collectively generated data, such as pairwise comparisons. Examples include political elections, ranking athletes based…
We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical…
This paper presents our studies on the rearrangement of links from the structure of websites for the purpose of improving the valuation of a page or group of pages as established by a ranking function as Google's PageRank. We build our…
We present exact results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific…