A surprising finding when analysing airport networks is the importance of Anchorage airport in Alaska. In fact, it is the most central airport in the network when applying betweenness! I do not believe this finding is completely accurate due to two reasons: (1) there is a potential for measurement error when not including tie weights (i.e., assigning the same importance to the connection between London Heathrow and New York’s JFK as to the connection between Pack Creek Airport and Sitka Harbor Sea Plane Base in Alaska), and (2) relying on US data only leads to sample selection as the airport network is a global system. This post highlights how to use a weighted betweenness measure as well as the extent of the sample selection issue.
A central metric in network research is the number of ties each node has, degree. Degree has been generalised to weighted networks as the sum of tie weights (Barrat et al., 2004), and as a function of the number of ties and the sum of their weights (Opsahl et al., 2010). However, all these measures are insensitive to variation in the tie weights. As such, the two nodes in this diagram would always have the same degree score. This post showcases a new measure that uses a tuning parameter to control whether variation should be taken favourable or discount the degree centrality score of a focal node.
A paper called “For the few not the many? The effects of affirmative action on presence, prominence, and social capital of women directors in Norway” that I have co-authored will be published in the Scandinavian Journal of Management. Governments have implemented various affirmative action policies to address vertical sex segregation in organizations. A gender representation law was introduced in Norway, which required public limited companies’ boards to have at least 40 percent representation of each sex by 2008. This law acted as an external shock, and this paper aims to explore its effects. In particular, it explores the gender bias, the emergence and sex of prominent directors, and directors’ social capital. We utilize data from May 2002 to August 2009 to analyze these aspects. The implied intention of the law was to create a larger pool of women acting as directors on boards, and the law has had the effect of increasing the representation of women on boards. However, it has also created a small elite of women directors who rank among the top on a number of proxies of influence.
A paper called “Node centrality in weighted networks: Generalizing degree and shortest paths” that I have co-authored will be published in Social Networks. Ties often have a strength naturally associated with them that differentiate them from each other. Tie strength has been operationalized as weights. A few network measures have been proposed for weighted networks, including three common measures of node centrality: degree, closeness, and betweenness. However, these generalizations have solely focused on tie weights, and not on the number of ties, which was the central component of the original measures. This paper proposes generalizations that combine both these aspects. We illustrate the benefits of this approach by applying one of them to Freeman’s EIES dataset.
A key node centrality measure in networks is closeness centrality (Freeman, 1978; Wasserman and Faust, 1994). It is defined as the inverse of farness, which in turn, is the sum of distances to all other nodes. As the distance between nodes in disconnected components of a network is infinite, this measure cannot be applied to networks with disconnected components (Opsahl et al., 2010; Wasserman and Faust, 1994). This post highlights a possible work-around, which allows the measure to be applied to these networks and at the same time maintain the original idea behind the measure.
This post explores the relationship between node degree and node strength in an online social network. In the online social network, heterogeneity in nodes’ average tie weight across different levels of degree had been reported. Although degree and average tie weight are significantly correlated, this post argues for the similarity of degree and node strength. In particular, high pair-wise correlation between degree and strength is found. In addition, power-law exponents of degree distributions and strength distribution are reported. The exponents are strikingly similar, in fact, they are almost identical.
tnet is a package written in R that can calculate weighted social network measures. Almost all of the ideas posted on this blog are related to weighted networks as, I believe, taking into consideration tie weights enables us to uncover and study interesting network properties. Not only are few social network measures applicable to weighted networks, but there is also a lack of software programmes that can analyse this type of networks. In fact, there are no open-source programmes. This hinders the use and development of weighted measures. tnet represents a first step towards creating such a programme. Through this platform, weighted network measures can easily be applied, and new measures easily implemented and distributed.
The content of this post has been integrated in the tnet manual, see Software.