Related papers: De-anonymizing scale-free social networks by perco…

Following the trend of data trading and data publishing, many online social networks have enabled potentially sensitive data to be exchanged or shared on the web. As a result, users' privacy could be exposed to malicious third parties since…

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…

In this paper we present new methods of measuring polarisation in social networks. We use Random Dot Product Graphs to embed social networks in metric spaces. Singular Value Decomposition of this social network then provider an embedded…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

While node semantics have been extensively explored in social networks, little research attention has been paid to profile edge semantics, i.e., social relations. Ideal edge semantics should not only show that two users are connected, but…

We consider a non-projective class of inhomogeneous random graph models with interpretable parameters and a number of interesting asymptotic properties. Using the results of Bollob\'as et al. [2007], we show that i) the class of models is…

In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific…

Having in mind the large-scale analysis of gene regulatory networks, we review a graph decimation algorithm, called "leaf-removal", which can be used to evaluate the feedback in a random graph ensemble. In doing this, we consider the…

We introduce a new kind of percolation on finite graphs called jigsaw percolation. This model attempts to capture networks of people who innovate by merging ideas and who solve problems by piecing together solutions. Each person in a social…

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…

A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…

The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in…

A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free…

We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…

We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network…

In this paper, we propose a new graph sampling method for online social networks that achieves the following. First, a sample graph should reflect the ratio between the number of nodes and the number of edges of the original graph. Second,…

Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a…

We propose a renormalization group treatment of stochastically growing networks. As an example, we study percolation on growing scale-free networks in the framework of a real-space renormalization group approach. As a result, we find that…

Triangles are an important building block and distinguishing feature of real-world networks, but their structure is still poorly understood. Despite numerous reports on the abundance of triangles, there is very little information on what…

A social network (SN) is a social structure consisting of a group representing the interaction between them. SNs have recently been widely used and, subsequently, have become suitable and popular platforms for product promotion and…