Temporal networks, whose network topology changes over time, are used to represent, e.g., opportunistic mobile networks, vehicle networks, and social contact networks, where two mobile devices (autos or individuals) are connected only when they are close to (interact with) each other. Such networks facilitate the transfer of information. In this paper, we address the problem of navigation on temporal networks: how to route a traffic demand from a source s to a destination d at time ts, based on the network observed before ts? Whenever the node hosting the information has a contact or interacts with another node, the routing method has to decide whether the information should be forwarded to the contacted node or not. Once the information is forwarded, the contacted node becomes the only node hosting the information. Firstly, we introduce a framework of designing navigation algorithms, in which a distance metric is defined and computed between any node to the target d based on the network observed before ts. Whenever a hosting node has a contact, it forwards the information to the contacted node if the contacted node is closer to the target than the hosting node according to the distance metric. Secondly, we propose systematically distance metrics of a node pair in the temporal network observed, that capture different network properties of a node pair. Thirdly, these metrics or routing strategies are evaluated in empirical contact networks, from the perspective of the time duration of the routing and the probability that the destination can be reached. Their performance is further explained via the correlation between distance metrics and the stability of each metric in ranking nodes’ distance to a target node. This work may serve as inspiration for evaluating and redesigning these strategies in other types of networks beyond physical contact networks.

Community detection of temporal (time-evolving) bipartite networks is challenging because it can be performed either on the temporal bipartite network, or on various projected networks, composed of only one type of nodes, via diverse community detection algorithms. In this paper, we aim to systematically design detection methods addressing both network choices and community detection algorithms, and to compare the community structures detected by different methods. We illustrate our methodology by using a telecommunications network as an example. We find that three methods proposed identify evident community structures: one is performed on each snapshot of the temporal network, and the other two, in temporal projections. We characterise the community structures detected by each method by an evaluation network in which the nodes are the services of the telecommunications network, and the weight of the links between them are the number of snapshots that both services were assigned to the same community. Analysing the evaluation networks of the three methods reveals the similarity and difference among these methods in identifying common node pairs or groups of nodes that often belong to the same community. We find that the two methods that are based on the same projected network identify consistent community structures, whereas the method based on the original temporal bipartite network complements this vision of the community structure. Moreover, we found a non-trivial number of node pairs that belong consistently to the same community in all the methods applied.

Multiple network embedding algorithms have been proposed to perform the prediction of missing or future links in complex networks. However, we lack the understanding of how network topology affects their performance, or which algorithms are more likely to perform better given the topological properties of the network. In this paper, we investigate how the clustering coefficient of a network, i.e., the probability that the neighbours of a node are also connected, affects network embedding algorithms’ performance in link prediction, in terms of the AUC (area under the ROC curve). We evaluate classic embedding algorithms, i.e., Matrix Factorisation, Laplacian Eigenmaps and node2vec, in both synthetic networks and (rewired) real-world networks with variable clustering coefficient. Specifically, a rewiring algorithm is applied to each real-world network to change the clustering coefficient while keeping key network properties. We find that a higher clustering coefficient tends to lead to a higher AUC in link prediction, except for Matrix Factorisation, which is not sensitive to the change of clustering coefficient. To understand such influence of the clustering coefficient, we (1) explore the relation between the link rating (probability that a node pair is the missing link) derived from the aforementioned algorithms and the number of common neighbours of the node pair, and (2) evaluate these embedding algorithms’ ability to reconstruct the original training (sub)network. All the network embedding algorithms that we tested tend to assign higher likelihood of connection to node pairs that share an intermediate or high number of common neighbours, independently of the clustering coefficient of the training network. Then, the predicted networks will have more triangles, thus a higher clustering coefficient. As the clustering coefficient increases, all the algorithms but Matrix Factorisation could also better reconstruct the training network. These two observations may partially explain why increasing the clustering coefficient improves the prediction performance.