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Ebook Computational network science - An algorithmic approach: Part 2

(BQ) Until now, studies in network science have been focused on particular relationships that require varied and sometimes-incompatible datasets, which has kept it from being a truly universal discipline. This new approach would remove the need for tedious human-based analysis of different datasets and help researchers spend more time on the qualitative aspects of network science research. Computational network science | CHAPTER 6 Diffusion and Contagion This chapter explores the phenomena of rampant changes in networks exemplified by (a) disseminations of preferences, (b) percolation, (c) epidemic (i.e., contagion) of disease, and (d) community compositions. The rest of this chapter reviews these four categories in order. 6.1  POPULATION PREFERENCE SPREAD Schelling’s (1971) residential neighborhood segregation model is the earliest formally studied report of rampant changes in networks. Schelling pointed out that a small preference for one’s neighbors to be of the same ethnicity leads to a widespread segregation emergent in the network. He used coins on a patch of graph paper to demonstrate this theory by placing pennies and nickels in different patterns on the cells. Coins were moved one by one if they were in an unsatisfactory composition. For every colored cell, if there were greater than 33% of the adjacent cells that were of a different color, the cell would move to another randomly selected cell. You can try the model out using Chris Cook’s online demonstration program or the NetLogo model. Further details and interesting emergent patterns that arise are available from Hatna and Benenson (2012). Let N be the population size and p be the uniform, random probability for the existence of a tie for each individual with another person in the network. Let us ignore the repeated connections. With the small value of p and the large value of N, PN represents the probability of an individual’s indirect connection with others in the network, that is, the second-hand tie through the individual’s primary tie. The expected (i.e., average) number of individuals that can be reached is shown by Equation 6.1. With the values of PN ≥ 0, contagion begins, that is, epidemic occurs. Rapid spread of diseases through connections in populations (e.g., obesity) is an epidemic and pandemic (i.e., an epidemic across borders) event (Hays, 2005). Topologies of networks may hinder or promote these .