Networks has the potential to increase the explanatory power of models. The content of this post, and accompanying paper, quantifies the size of this effect for predicting the financial health of companies. It is my hope that it can help drive more research into networks and enable more organizations to develop better models and understand interdependencies to a greater extent. Companies do not operate in a vacuum. As companies move towards an increasingly specialized production function and ...| Tore Opsahl
A paper called "Triadic closure in two-mode networks: Redefining the global and local clustering coefficients" that I have authored will be published in the special issue of Social Networks on two-mode networks (2012). As the vast majority of network measures are defined for one-mode networks, two-mode networks often have to be projected onto one-mode networks to be analyzed. A number of issues arise in this transformation process, especially when analyzing ties among nodes' contacts. For exa...| Tore Opsahl
R is a great tool for analysing data with an intuitive and interactive programming language. There are a number of limitations with an interactive programming language compared to compiled languages, such as higher memory and processing requirements. One way of overcoming these requirements is to use cloud computing, such as Amazon EC2. The Bioconductor group has an Amazon Machine Image with the latest version of R and RStudio; however, there is a major security hole in the default setup that...| Tore Opsahl
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 Harbo...| Tore Opsahl
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 co...| Tore Opsahl
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 representat...| Tore Opsahl
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 sol...| Tore Opsahl
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 applie...| Tore Opsahl
Similar to the motivation of the global clustering coefficient that I proposed in Clustering in two-mode networks, the local clustering coefficient is biased if applied to a projection of a two-mode network. It is biased in the sense that the randomly expected value is not obtained on the projection of a random two-mode network. To […]| Tore Opsahl
The Online Social Network-dataset used in my Ph.D. thesis is now available on the Dataset-page. This network has also been described in Patterns and Dynamics of Users’ Behaviour and Interaction: Network Analysis of an Online Community and used in Prominence and control: The weighted rich-club effect and Clustering in weighted networks. The network originate from […]| Tore Opsahl
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 distribut...| Tore Opsahl
Many network dataset are by definition two-mode networks. Yet, few network measures can be directly applied to them. Therefore, two-mode networks are often projected onto one-mode networks by selecting a node set and linking two nodes if they were connected to common nodes in the two-mode network. This process has a major impact on the […]| Tore Opsahl
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 […]| Tore Opsahl
In this post, I extend the Weighted Rich-club Effect by suggesting and testing a different null model for the scientific collaboration network (Newman, 2001). This network is a two-mode network, which becomes an undirected one-mode network when projected. In the paper, we compared the observed weighted rich-club coefficient with the one found on random networks. […]| Tore Opsahl
I have now completed my Ph.D. at the School of Business and Management of Queen Mary College, University of London. My Ph.D. programme was defined around a number of projects, which drew on, and extended, recent theoretical and methodological advances in network science. The projects that were concerned with weighted networks and longitudinal networks were […]| Tore Opsahl
This post highlights a number of methods for projecting both binary and weighted two-mode networks (also known as affiliation or bipartite networks) onto weighted one-mode networks. Although I would prefer to analyse two-mode networks in their original form, few methods exist for that purpose. These networks can be transformed into one-mode networks by projecting them […]| Tore Opsahl
A key assumption of Granovetter’s (1973) Strength of Weak Ties theory is that strong ties are embedded by being part of triangles, whereas weak ties are not embedded by being created towards disconnected nodes. This assumption have been tested by calculating the traditional clustering coefficient on binary networks created with increasing cut-off parameters (i.e., creating […]| Tore Opsahl
A paper called "Clustering in Weighted Networks" that I have co-authored will be published in Social Networks. Although many social network measures exist for binary networks and many theories differentiate between strong and weak ties, few measures have been generalised so that they can be applied to weighted networks and retain the information encoded in the weights of ties. One of these measures is the global clustering coefficient, which measures embeddedness or, more specifically, the li...| Tore Opsahl
Recently, a number of network dataset have been constructed from archival data (e.g., email logs) with the aim to study human interaction. This has allowed researchers to study large-scale social networks. If the archival data does not included information about the severing or weakening of ties, non-relevant interaction among people, which occurred far in the […]| Tore Opsahl
A paper called "Patterns and Dynamics of Users' Behaviour and Interaction: Network Analysis of an Online Community" that I have co-authored will be published in the Journal of the American Society for Information Science and Technology (JASIST). In this paper, we studied the evolution of a variety of properties in an online community, including how users create, reciprocate, and deepen relationships with one another, variations in users’ gregariousness and popularity, reachability and typic...| Tore Opsahl
This post highlights a generalisation of Freeman’s (1978) betweenness measure to weighted networks implicitly introduced by Brandes (2001) when he developed an algorithm for calculating betweenness faster. Betweenness is a measure of the extent to which a node funnels transactions among all the other nodes in the network. By funnelling the transactions, a node can […]| Tore Opsahl
The method used to operationalise ties’ strength into weights affects the outcomes of weighted networks measures. Simply assigning 1, 2, and 3 to three different levels of tie strength might not be appropriate as this scale might misrepresent the actually difference among the three levels (using an ordinal scale). In this post, I highlight issues […]| Tore Opsahl
The generalisation of the local clustering coefficient to weighted networks by Barrat et al. (2004) considers the value of a triplet to be the average of the weights attached to the two ties that make up the triplet. In this post, I suggest three additional methods for defining the triplet value. The content […]| Tore Opsahl
The average distance that separate nodes in a network became a famous measure following Milgram’s six-degrees of separation experiment in 1967 that found that people in the US were on average…| Tore Opsahl
This post proposes a local (node-level) version of the Weighted Rich-club Effect (PRL 101, 168702). By incorporating this measure into a regression analysis, the impact of targeting efforts towards…| Tore Opsahl
