Research Seminar – Des Higham

Mutual Reinforcement in Network Science

Des Higham – Numerical Analysis, University of Edinburgh

Thursday 23rd January 4pm – Inspace, 1 Crichton St

Larry Page and Sergey Brin developed the Google PageRank algorithm to “bring order to the web.” Their key insight was to define a page as important if it was pointed to by many important pages. Although it may seem like an exercise in circular reasoning, this approach led to a practical and effective methodology. In fact, the idea can be traced back to algorithms proposed in the 19th century for ranking players in chess tournaments. This talk described two recent applications of this “mutually reinforcing” philosophy. First it looked at the Friendship Paradox, formalised by the sociologist Scott Feld in 1991, which states that “on average our friends have more friends than us.” The observation has spawned a range of activity in quantitative network science, and may explain reports of increasing levels of dissatisfaction in online social interaction. More positively, the paradox can be leveraged in order to detect the spread of information or disease, and to drive effective network interventions. It looked at generalisations of the original Friendship Paradox that address questions such as “are our friends more important than us?” and “do our followers have more followers than us?” Second, it considered the concept of a clustering coefficient, which was formalised in a seminal 1998 paper of Watts and Strogatz. This quantity measures whether nodes in a network tend to create tightly knit groups, characterised by a relatively high density of triangles. It will explain how a mutually reinforcing analogue can be defined, thereby identifying influential triangles in a network.

Des Higham, FRSE, is Professor of Numerical Analysis in the School of Mathematics at the University of Edinburgh. He has research interests in stochastic computation, with applications in sociological & technological networks, future cities and computational biology. He is an EPSRC/RCUK Digital Economy Established Career Fellow and is the Edinburgh lead on the EPSRC Programme Grant “Inference, Computation and Numerics for Insights into Cities” (ICONIC).

Inspace, 1 Crichton St, Edinburgh EH8 9AB