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We address the problem of link reciprocity, the non-random presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation…

Disordered Systems and Neural Networks · Physics 2007-05-23 Diego Garlaschelli , Maria I. Loffredo

Network science have constantly been in the focus of research for the last decade, with considerable advances in the controllability of their structural. However, much less effort has been devoted to study that how to improve the…

Systems and Control · Computer Science 2016-10-12 Jiuqiang Xu , Jinfa Wang , Hai Zhao , Siyuan Jia

Link prediction algorithms can help to understand the structure and dynamics of complex systems, to reconstruct networks from incomplete data sets and to forecast future interactions in evolving networks. Available algorithms based on…

Social and Information Networks · Computer Science 2020-11-19 Alberto Aleta , Marta Tuninetti , Daniela Paolotti , Yamir Moreno , Michele Starnini

Link prediction has aroused extensive attention since it can both discover hidden connections and predict future links in the networks. Many unsupervised link prediction algorithms have been proposed to find these links in a variety of…

Social and Information Networks · Computer Science 2021-05-10 Jingwei Wang , Yunlong Ma , Yun Yuan

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…

Probability · Mathematics 2015-03-18 Emmanuel Jacob , Peter Mörters

To evaluate the performance of prediction of missing links, the known data are randomly divided into two parts, the training set and the probe set. We argue that this straightforward and standard method may lead to terrible bias, since in…

Data Analysis, Statistics and Probability · Physics 2015-05-27 Yu-Xiao Zhu , Linyuan Lü , Qian-Ming Zhang , Tao Zhou

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…

Discrete Mathematics · Computer Science 2015-09-30 Kevin E. Bassler , Charo I. Del Genio , Péter L. Erdős , István Miklós , Zoltán Toroczkai

Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…

Statistical Mechanics · Physics 2007-05-23 F. Stauffer

Over the past years, embedding learning on networks has shown tremendous results in link prediction tasks for complex systems, with a wide range of real-life applications. Learning a representation for each node in a knowledge graph allows…

Machine Learning · Computer Science 2026-02-03 Orell Trautmann , Olaf Wolkenhauer , Clémence Réda

Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment (UA) rules. When a new edge is created, with probability $p\in [0,1]$, it follows…

Social and Information Networks · Computer Science 2021-01-19 Tiandong Wang , Panpan Zhang

We analyze whether preferential attachment in scientific coauthorship networks is different for authors with different forms of centrality. Using a complete database for the scientific specialty of research about "steel structures," we show…

Social and Information Networks · Computer Science 2012-02-03 Alireza Abbasi , Liaquat Hossain , Loet Leydesdorff

Link and sign prediction in complex networks bring great help to decision-making and recommender systems, such as in predicting potential relationships or relative status levels. Many previous studies focused on designing the special…

Physics and Society · Physics 2021-08-04 Chuang Liu , Shimin Yu , Ying Huang , Zi-Ke Zhang

We consider the estimation of the affine parameter (and power-law exponent) in the preferential attachment model with random initial degrees. We derive the likelihood, and show that the maximum likelihood estimator (MLE) is asymptotically…

Statistics Theory · Mathematics 2017-03-09 Fengnan Gao , Aad van der Vaart

Network science is a powerful framework allowing to model complex systems, it is capable to describe and take into account the intricate web of connections existing among the constituting basic element of the system. Recently scholars have…

Statistical Mechanics · Physics 2026-05-19 Diego Febbe , Duccio Fanelli , Timoteo Carletti

Preferential attachment lies at the heart of many network models aiming to replicate features of real world networks. To simulate the attachment process, conduct statistical tests, or obtain input data for benchmarks, efficient algorithms…

Data Structures and Algorithms · Computer Science 2023-01-18 Daniel Allendorf , Ulrich Meyer , Manuel Penschuck , Hung Tran

Predicting edges in networks is a key problem in social network analysis and involves reasoning about the relationships between nodes based on the structural properties of a network. In particular, link prediction can be used to analyse how…

Social and Information Networks · Computer Science 2020-01-01 Mateusz Tarkowski , Tomasz Michalak , Michael Wooldridge

In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…

Combinatorics · Mathematics 2020-08-25 Samuel , G. Balogh , Gergely Palla , Ivan Kryven

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…

Physics and Society · Physics 2016-02-02 Konstantin Zuev , Fragkiskos Papadopoulos , Dmitri Krioukov

Link prediction is a technique that uses the topological information in a given network to infer the missing links in it. Since past research on link prediction has primarily focused on enhancing performance for given empirical systems,…

Physics and Society · Physics 2015-03-11 Min-Woo Ahn , Woo-Sung Jung

Link prediction, a foundational task in complex network analysis, has extensive applications in critical scenarios such as social recommendation, drug target discovery, and knowledge graph completion. However, existing evaluations of…

Other Statistics · Statistics 2025-12-30 Yilin Bi , Junhao Bian , Shuyan Wan , Shuaijia Wang , Tao Zhou