Abstract: We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age. As a special example of the latter we consider mixing according to vertex degree, i.e., according to the number of connections vertices have to other vertices: do gregarious people tend to associate with other gregarious people? We propose a number of measures of assortative mixing appropriate to the various mixing types, and apply them to a variety of real-world networks, showing that assortative mixing is a pervasive phenomenon found in many networks. We also propose several models of assortatively mixed networks, both analytic ones based on generating function methods, and numerical ones based on Monte Carlo graph generation techniques. We use these models to probe the properties of networks as their level of assortativity is varied. In the particular case of mixing by degree, we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices.

Abstract: Finding the right horse for each rider is a difficult task as it is just as important that the temperament of the horse fits the rider as it is that the horse is of the right size. Even though it is a commonly experienced problem, no objective method of easily measuring the horse“s temperament has yet been developed. If it is possible to test horses and get an objective measure of how reactive (emotional) they are, it could be a big help in finding the right horse for each rider. It would be desirable to have a way of testing the horse”s reaction in an unfamiliar (and potentially frightening) situation. In practice this test should be just as easy as it is getting a judgement of its conformation and gaits.
The aim of the present study was to measure individual variation in HR response to different novel objects in horses of the same age, breed and reared in the same environment. We wanted to see whether certain horses (i.e. more emotional horses) react more to novel stimuli, in general, than other horses (i.e. less emotional), irrespective of the type of stimulus. We also wanted to see if different novel stimuli elicited different responses within individuals. The hypothesis was that individuals will react in a similar way to various stimuli.
Twenty four Danish warmblood horses were included in this study. All horses were 2 year-old stallions, reared under similar environmental conditions. They had received a minimum of handling prior to the experimental period. Three different stimuli were used. They were chosen because they were novel to the horses and would elicit measurable fear-reactions in all horses, but not so much that the horses did not approach the feed within the duration of the test. The visual stimulus consisted of a 1meter high orange traffic cone with reflex stripes, placed 1 m in front of the tub, the olfactory stimulus was eucalyptus oil and the auditory stimulus was a radio tuned to white noise. The control was an empty arena.
The result was that only the HR response to the auditory and visual stimuli differed significantly from the control days. The olfactory stimulus did not seem to alarm the horses the way the other stimuli did. We found a tendency towards a correlation in reaction between the olfactory and auditory stimuli and between the auditory and visual stimuli within individuals. These results indicate that horses do not generalize completely in their reaction between different stimuli.