Social networks have been of much interest in recent years. We here focus on a network structure derived from co-occurrences of people in traditional newspaper media. We find three clear deviations from what can be expected in a random graph. First, the average degree in the empirical network is much lower than expected, and the average weight of a link much higher than expected. Secondly, high degree nodes attract disproportionately much weight. Thirdly, relatively much of the weight seems to concentrate between high degree nodes. We believe this can be explained by the fact that most people tend to co-occur repeatedly with the same people. We create a model that replicates these observations qualitatively based on two self-reinforcing processes: (1) more frequently occurring persons are more likely to occur again; and (2) if two people co-occur frequently, they are more likely to co-occur again. This suggest that the media tends to focus on people that are already in the news, and that they reinforce existing co-occurrences.