Related papers: Network Essence: PageRank Completion and Centralit…
The well-known statistic PageRank was created in 1998 by co-founders of Google, Sergey Brin and Larry Page, to optimize the ranking of websites for their search engine outcomes. It is computed using an iterative algorithm, based on the idea…
Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and…
The importance of modeling and analyzing Social Networks is a consequence of the success of Online Social Networks during last years. Several models of networks have been proposed, reflecting the different characteristics of Social…
This article focuses on the problem of studying shared- and individual-specific structure in replicated networks or graph-valued data. In particular, the observed data consist of $n$ graphs, $G_i, i=1,\ldots,n$, with each graph consisting…
In this paper we analyze the PageRank of a complex network as a function of its personalization vector. By using this approach, a complete characterization of the existence and uniqueness of fixed points of PageRank of a graph is given in…
We consider the so-called GI/GI/N queueing network in which a stream of jobs with independent and identically distributed service times arrive according to a renewal process to a common queue served by $N$ identical servers in a…
Many systems, including the Internet, social networks, and the power grid, can be represented as graphs. When analyzing graphs, it is often useful to compute scores describing the relative importance or distance between nodes. One example…
The human brain forms functional networks on all spatial scales. Modern fMRI scanners allow to resolve functional brain data in high resolutions, allowing to study large-scale networks that relate to cognitive processes. The analysis of…
We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
PageRank is arguably the most popular ranking algorithm which is being applied in real systems ranging from information to biological and infrastructure networks. Despite its outstanding popularity and broad use in different areas of…
Connection matrices for graph parameters with values in a field have been introduced by M. Freedman, L. Lov{\'a}sz and A. Schrijver (2007). Graph parameters with connection matrices of finite rank can be computed in polynomial time on graph…
Multiplex networks are generalized network structures that are able to describe networks in which the same set of nodes are connected by links that have different connotations. Multiplex networks are ubiquitous since they describe social,…
Knowledge graphs have evolved rapidly in recent years and their usefulness has been demonstrated in many artificial intelligence tasks. However, knowledge graphs often have lots of missing facts. To solve this problem, many knowledge graph…
Patterns often appear in a variety of large, real-world networks, and interesting physical phenomena are often explained by network topology as in the case of the bow-tie structure of the World Wide Web, or the small world phenomenon in…
The MBTI personality test and a personal facebook network were used in order to gain some insights on the relationship of social network centrality and path length measures and different personality types. Although the personality…
Since the advent of the Internet, quantifying the relative importance of web pages is at the core of search engine methods. According to one algorithm, PageRank, the worldwide web structure is represented by the Google matrix, whose…
Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks.…