Related papers: Revisiting Network Value: Sublinear Knowledge Law
How do complex social systems evolve in the modern world? This question lies at the heart of social physics, and network analysis has proven critical in providing answers to it. In recent years, network analysis has also been used to gain a…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
In their recent work "Scale-free networks are rare", Broido and Clauset address the problem of the analysis of degree distributions in networks to classify them as scale-free at different strengths of "scale-freeness." Over the last two…
We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…
In this paper we investigate the value of a social network with respect to the probability mechanism underlying its structure. Specifically, we compute the value for small world and scale free networks. We provide evidence in support of the…
Heterogeneous nature of real networks implies that different edges play different roles in network structure and functions, and thus to identify significant edges is of high value in both theoretical studies and practical applications. We…
We propose an analysis of the codified Law of France as a structured system. Fifty two legal codes are selected on the basis of explicit legal criteria and considered as vertices with their mutual quotations forming the edges in a network…
Subgraphs are very important for understanding structure and function of complex networks. Dyad and triad are the elementary subgraphs. We focus on the distribution of their act degree defined as the number of activities, events or…
Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks…
In many scenarios, networks emerge endogenously as cognitive agents establish links in order to exchange information. Network formation has been widely studied in economics, but only on the basis of simplistic models that assume that the…
Deep learning has been successfully applied to various tasks, but its underlying mechanism remains unclear. Neural networks associate similar inputs in the visible layer to the same state of hidden variables in deep layers. The fraction of…
Benford's Law (BL) or the Significant Digit Law defines the probability distribution of the first digit of numerical values in a data sample. This Law is observed in many naturally occurring datasets. It can be seen as a measure of…
Citation networks emerge from a number of different social systems, such as academia (from published papers), business (through patents) and law (through legal judgements). A citation represents a transfer of information, and so studying…
Road network representation learning aims to learn compressed and effective vectorized representations for road segments that are applicable to numerous tasks. In this paper, we identify the limitations of existing methods, particularly…
In this paper, we explore the consequences of a distinction between `live' and `dead' network nodes; `live' nodes are able to acquire new links whereas `dead' nodes are static. We develop an analytically soluble growing network model…
Power law degree distribution was shown in many complex networks. However, in most real systems, deviation from power-law behavior is observed in social and economical networks and emergence of giant hubs is obvious in real network…
There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…
A concept of higher order neighborhood in complex networks, introduced previously (PRE \textbf{73}, 046101, (2006)), is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each…
With good explanatory power and controllability, rule-based methods play an important role in many tasks such as knowledge reasoning and decision support. However, existing studies primarily focused on learning chain-like rules, which limit…
About two million U.S. corporations and partnerships are linked to each other and human investors by about 15 million owner-subsidiary links. Comparable social networks such as corporate board memberships and socially-built systems such as…