A Faster Method to Estimate Closeness Centrality Ranking

Closeness centrality is one way of measuring how central a node is in the given network. The closeness centrality measure assigns a centrality value to each node based on its accessibility to the whole network. In real life applications, we are mainly interested in ranking nodes based on their centrality values. The classical method to compute the rank of a node first computes the closeness centrality of all nodes and then compares them to get its rank. Its time complexity is $O(n \cdot m + n)$, where $n$ represents total number of nodes, and $m$ represents total number of edges in the network. In the present work, we propose a heuristic method to fast estimate the closeness rank of a node in $O(\alpha \cdot m)$ time complexity, where $\alpha = 3$. We also propose an extended improved method using uniform sampling technique. This method better estimates the rank and it has the time complexity $O(\alpha \cdot m)$, where $\alpha \approx 10-100$. This is an excellent improvement over the classical centrality ranking method. The efficiency of the proposed methods is verified on real world scale-free social networks using absolute and weighted error functions

Degree Ranking Using Local Information

Most real world dynamic networks are evolved very fast with time. It is not feasible to collect the entire network at any given time to study its characteristics. This creates the need to propose local algorithms to study various properties of the network. In the present work, we estimate degree rank of a node without having the entire network. The proposed methods are based on the power law degree distribution characteristic or sampling techniques. The proposed methods are simulated on synthetic networks, as well as on real world social networks. The efficiency of the proposed methods is evaluated using absolute and weighted error functions. Results show that the degree rank of a node can be estimated with high accuracy using only $1\%$ samples of the network size. The accuracy of the estimation decreases from high ranked to low ranked nodes. We further extend the proposed methods for random networks and validate their efficiency on synthetic random networks, that are generated using Erd\H{o}s-R\'{e}nyi model. Results show that the proposed methods can be efficiently used for random networks as well

A Survey on Studying the Social Networks of Students

Do studies show that physical and online students' social networks support education? Analyzing interactions between students in schools and universities can provide a wealth of information. Studies on students' social networks can help us understand their behavioral dynamics, the correlation between their friendships and academic performance, community and group formation, information diffusion, and so on. Educational goals and holistic development of students with various academic abilities and backgrounds can be achieved by incorporating the findings attained by the studies in terms of knowledge propagation in classroom and spread of delinquent behaviors. Moreover, we use Social Network Analysis (SNA) to identify isolated students, ascertain the group study culture, analyze the spreading of various habits like smoking, drinking, and so on. In this paper, we present a review of the research showing how analysis of students' social networks can help us identify how improved educational methods can be used to make learning more inclusive at both school and university levels and achieve holistic development of students through expansion of their social networks, as well as control the spread of delinquent behaviors.Comment: Huso 201