Non-Conservative Diffusion and its Application to Social Network Analysis

The random walk is fundamental to modeling dynamic processes on networks. Metrics based on the random walk have been used in many applications from image processing to Web page ranking. However, how appropriate are random walks to modeling and analyzing social networks? We argue that unlike a random walk, which conserves the quantity diffusing on a network, many interesting social phenomena, such as the spread of information or disease on a social network, are fundamentally non-conservative. When an individual infects her neighbor with a virus, the total amount of infection increases. We classify diffusion processes as conservative and non-conservative and show how these differences impact the choice of metrics used for network analysis, as well as our understanding of network structure and behavior. We show that Alpha-Centrality, which mathematically describes non-conservative diffusion, leads to new insights into the behavior of spreading processes on networks. We give a scalable approximate algorithm for computing the Alpha-Centrality in a massive graph. We validate our approach on real-world online social networks of Digg. We show that a non-conservative metric, such as Alpha-Centrality, produces better agreement with empirical measure of influence than conservative metrics, such as PageRank. We hope that our investigation will inspire further exploration into the realms of conservative and non-conservative metrics in social network analysis

Social Interactions and Economic Behavior

This paper is a critical introduction to the new wave of economic literature on the effect of social interactions on individual behavior and aggregate economic outcomes. I refer to this research program, also known as new social economics, as the socioeconomic analysis of behavior, to distinguish it from the more popular economic analysis of social behavior. I discuss the main features of so-called interactions-based models, and I show how they help us to understand substantive economic phenomena. In order to restrict the focus, I choose five possible applications: matching in the labor market, welfare participation, poverty traps and inequality, investor behavior, and consumer behavior. Then I dwell upon two key undecided questions: (i) why economic behavior is affected by social interactions, and (ii) how the social context is shaped by rational individuals. Finally, I briefly discuss the main empirical routes so far used.new social economics, social interactions, neighborhood effects, social networks, social norms, social multiplier

Mathematical evolution in discrete networks

This paper provides a mathematical explanation for the phenomenon of \triadic closure" so often seen in social networks. It appears to be a natural consequence when network change is constrained to be continuous. The concept of chordless cycles in the network's \irreducible spine" is used in the analysis of the network's dynamic behavior. A surprising result is that as networks undergo random, but continuous, perturbations they tend to become more structured and less chaotic

A Relational Hyperlink Analysis of an Online Social Movement

In this paper we propose relational hyperlink analysis (RHA) as a distinct approach for empirical social science research into hyperlink networks on the World Wide Web. We demonstrate this approach, which employs the ideas and techniques of social network analysis (in particular, exponential random graph modeling), in a study of the hyperlinking behaviors of Australian asylum advocacy groups. We show that compared with the commonly-used hyperlink counts regression approach, relational hyperlink analysis can lead to fundamentally different conclusions about the social processes underpinning hyperlinking behavior. In particular, in trying to understand why social ties are formed, counts regressions may over-estimate the role of actor attributes in the formation of hyperlinks when endogenous, purely structural network effects are not taken into account. Our analysis involves an innovative joint use of two software programs: VOSON, for the automated retrieval and processing of considerable quantities of hyperlink data, and LPNet, for the statistical modeling of social network data. Together, VOSON and LPNet enable new and unique research into social networks in the online world, and our paper highlights the importance of complementary research tools for social science research into the web

Measuring social dynamics in a massive multiplayer online game

Quantification of human group-behavior has so far defied an empirical, falsifiable approach. This is due to tremendous difficulties in data acquisition of social systems. Massive multiplayer online games (MMOG) provide a fascinating new way of observing hundreds of thousands of simultaneously socially interacting individuals engaged in virtual economic activities. We have compiled a data set consisting of practically all actions of all players over a period of three years from a MMOG played by 300,000 people. This large-scale data set of a socio-economic unit contains all social and economic data from a single and coherent source. Players have to generate a virtual income through economic activities to `survive' and are typically engaged in a multitude of social activities offered within the game. Our analysis of high-frequency log files focuses on three types of social networks, and tests a series of social-dynamics hypotheses. In particular we study the structure and dynamics of friend-, enemy- and communication networks. We find striking differences in topological structure between positive (friend) and negative (enemy) tie networks. All networks confirm the recently observed phenomenon of network densification. We propose two approximate social laws in communication networks, the first expressing betweenness centrality as the inverse square of the overlap, the second relating communication strength to the cube of the overlap. These empirical laws provide strong quantitative evidence for the Weak ties hypothesis of Granovetter. Further, the analysis of triad significance profiles validates well-established assertions from social balance theory. We find overrepresentation (underrepresentation) of complete (incomplete) triads in networks of positive ties, and vice versa for networks of negative ties...Comment: 23 pages 19 figure