Complex Networks from Classical to Quantum

Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information physics is setting the stage for a theory of complex systems with quantum information-inspired methods. Novel quantum induced effects have been predicted in random graphs---where edges represent entangled links---and quantum computer algorithms have been proposed to offer enhancement for several network problems. Here we review the results at the cutting edge, pinpointing the similarities and the differences found at the intersection of these two fields.Comment: 12 pages, 4 figures, REVTeX 4-1, accepted versio

Maximal entropy random walk in community finding

The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their key part is a (dis)similarity matrix, according to which nodes are grouped. This study encompasses the use of the stochastic matrix of a random walk, its mean first-passage time matrix, and a matrix of weighted paths count. We briefly indicate the connection between those quantities and propose substituting the maximal-entropy random walk for the previously chosen models. This unique random walk maximises the entropy of ensembles of paths of given length and endpoints, which results in equiprobability of those paths. We compare performance of the selected algorithms on LFR benchmark graphs. The results show that the change in performance depends very strongly on the particular algorithm, and can lead to slight improvements as well as significant deterioration.Comment: 7 pages, 4 figures, submitted to European Physical Journal Special Topics following the 4-th Conference on Statistical Physics: Modern Trends and Applications, July 3-6, 2012 Lviv, Ukrain

Distinguishing Topical and Social Groups Based on Common Identity and Bond Theory

Social groups play a crucial role in social media platforms because they form the basis for user participation and engagement. Groups are created explicitly by members of the community, but also form organically as members interact. Due to their importance, they have been studied widely (e.g., community detection, evolution, activity, etc.). One of the key questions for understanding how such groups evolve is whether there are different types of groups and how they differ. In Sociology, theories have been proposed to help explain how such groups form. In particular, the common identity and common bond theory states that people join groups based on identity (i.e., interest in the topics discussed) or bond attachment (i.e., social relationships). The theory has been applied qualitatively to small groups to classify them as either topical or social. We use the identity and bond theory to define a set of features to classify groups into those two categories. Using a dataset from Flickr, we extract user-defined groups and automatically-detected groups, obtained from a community detection algorithm. We discuss the process of manual labeling of groups into social or topical and present results of predicting the group label based on the defined features. We directly validate the predictions of the theory showing that the metrics are able to forecast the group type with high accuracy. In addition, we present a comparison between declared and detected groups along topicality and sociality dimensions.Comment: 10 pages, 6 figures, 2 table