Related papers: Schroedinger-like PageRank equation and localizati…
Higher-order networks are efficient representations of sequential data. Unlike the classic first-order network approach, they capture indirect dependencies between items composing the input sequences by the use of \textit{memory-nodes}. We…
We study the behavior of network diffusions based on the PageRank random walk from a set of seed nodes. These diffusions are known to reveal small, localized clusters (or communities) and also large macro-scale clusters by varying a…
The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…
The World Wide Web (WWW) is the repository of large number of web pages which can be accessed via Internet by multiple users at the same time and therefore it is Ubiquitous in nature. The search engine is a key application used to search…
Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world…
As the calculation of centrality in complex networks becomes increasingly vital across technological, biological, and social systems, precise and scalable ranking methods are essential for understanding these networks. This paper introduces…
To account for strong aging characteristics of citation networks, we modify Google's PageRank algorithm by initially distributing random surfers exponentially with age, in favor of more recent publications. The output of this algorithm,…
This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges…
Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…
During the last two decades, we easilly see that the World Wide Web's link structure is modeled as the directed graph. In this paper, we will model the World Wide Web's link structure as the directed hypergraph. Moreover, we will develop…
In network science, there is often the need to sort the graph nodes. While the sorting strategy may be different, in general sorting is performed by exploiting the network structure. In particular, the metric PageRank has been used in the…
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…
Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schr\"odinger equation. This equation is equivalent to a high-dimensional Helmholtz equation and it has solutions that are outgoing waves,…
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…
The dynamics of an initially localized Anderson mode is studied in the framework of the nonlinear Schroedinger equation in the presence of disorder. It is shown that the dynamics can be described in the framework of the Liouville operator.…
PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability…
The quantum version of Google PageRank has recently been investigated by various groups and shown to be quadratically faster in time than the classical PageRank algorithm. In this paper we propose the implementation of Quantum PageRank by a…
To rank nodes in quasi-hierarchical networks of social nature, it is necessary to carry out a detailed analysis of the network and evaluate the results obtained according to all the given criteria and identify the most influential nodes.…
The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs…
Link prediction in complex networks--identifying the missing or future connections--remains a cornerstone problem for understanding network evolution and function, yet existing methods struggle to balance computational efficiency with…