Anomalous connections in a computer network graph can be a signal of malicious behaviours. For instance, a compromised computer node tends to form a large number of new client edges in the network graph, connecting to server IP (Internet Protocol) addresses which have not previously been visited. This behaviour can be caused by malware (malicious software) performing a denial of service (DoS) attack, to cause disruption or further spread malware, alternatively, the rapid formation of new edges by a compromised node can be caused by an intruder seeking to escalate privileges by traversing through the host network. However, study of computer network flow data suggests new edges are also regularly formed by uninfected hosts, and often in bursts. Statistically detecting anomalous formation of new edges requires reliable models of the normal rate of new edges formed by each host. Network traffic data are complex, and so the potential number of variables which might be included in such a statistical model can be large, and without proper treatment this would lead to overfitting of models with poor predictive performance. In this paper, Bayesian variable selection is applied to a logistic regression model for new edge formation for the purpose of selecting the best subset of variables to include.