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A network has a non-overlapping community structure if the nodes of the network can be partitioned into disjoint sets such that each node in a set is densely connected to other nodes inside the set and sparsely connected to the nodes out-…
Random walks over directed graphs are used to model activities in many domains, such as social networks, influence propagation, and Bayesian graphical models. They are often used to compute the importance or centrality of individual nodes…
Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to…
Social networks are the social structures which are composed of people and their relationships and nowadays, play an important role in data extension. In such networks, the communities are recognized as the groups of users who are often…
We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…
How does one find important or influential people in an online social network? Researchers have proposed a variety of centrality measures to identify individuals that are, for example, often visited by a random walk, infected in an…
Centrality metrics are among the main tools in social network analysis. Being central for a user of a network leads to several benefits to the user: central users are highly influential and play key roles within the network. Therefore, the…
The notion of return probability -- explored most famously by George P\'{o}lya on d-dimensional lattices -- has potential as a measure for the analysis of networks. We present an efficient method for finding return probability distributions…
In this work we address the problem of detecting overlapping communities in social networks. Because the word "community" is an ambiguous term, it is necessary to quantify what it means to be a community within the context of a particular…
Spreading is a ubiquitous process in the social, biological and technological systems. Therefore, identifying influential spreaders, which is important to prevent epidemic spreading and to establish effective vaccination strategies, is full…
By drawing on large-scale online data we construct and analyze the time-varying worldwide network of professional relationships among start-ups. The nodes of this network represent companies, while the links model the flow of employees and…
Community identification is a long-standing challenge in the modern network science, especially for very large scale networks containing millions of nodes. In this paper, we propose a new metric to quantify the structural similarity between…
Community detection is the task of identifying clusters or groups of nodes in a network where nodes within the same group are more connected with each other than with nodes in different groups. It has practical uses in identifying similar…
In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the…
Effective mining of social media, which consists of a large number of users is a challenging task. Traditional approaches rely on the analysis of text data related to users to accomplish this task. However, text data lacks significant…
We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative…
The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness…
Nodes that play strategic roles in networks are called critical or influential nodes. For example, in an epidemic, we can control the infection spread by isolating critical nodes; in marketing, we can use certain nodes as the initial…
Community detection in social networks is a problem with considerable interest, since, discovering communities reveals hidden information about networks. There exist many algorithms to detect inherent community structures and recently few…
This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…