Benchmarking Measures of Network Influence

Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and $k$-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. We argue that the exhaustive approach of the TKO score makes it an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the common network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; however, temporal networks and the TKO measure provide the requisite targets for the hunt for effective predictive measures

Network robustness assessed within a dual connectivity framework : Joint dynamics of the Active and Idle Networks

Network robustness against attacks has been widely studied in fields as diverse as the Internet, power grids and human societies. But current definition of robustness is only accounting for half of the story: the connectivity of the nodes unaffected by the attack. Here we propose a new framework to assess network robustness, wherein the connectivity of the affected nodes is also taken into consideration, acknowledging that it plays a crucial role in properly evaluating the overall network robustness in terms of its future recovery from the attack. Specifically, we propose a dual perspective approach wherein at any instant in the network evolution under attack, two distinct networks are defined: (i) the Active Network (AN) composed of the unaffected nodes and (ii) the Idle Network (IN) composed of the affected nodes. The proposed robustness metric considers both the efficiency of destroying the AN and that of building-up the IN. We show, via analysis of well-known prototype networks and real world data, that trade-offs between the efficiency of Active and Idle Network dynamics give rise to surprising robustness crossovers and re-rankings, which can have significant implications for decision making

Peer review networks between Bitcoin traders

Bitcoin is a cryptocurrency that can be traded online. Some of the online Bitcoin trading platforms allow traders to give trust ratings to each other. Trust ratings are meant to indicate with whom to trade. Given and received trust ratings between Bitcoin traders form a Bitcoin trader peer review network. Understanding the functionality of Bitcoin peer review networks is crucial due to counter-party risk in Bitcoin transactions. This work studies the social aspects of Bitcoin trading. Trust rating data from two online Bitcoin trading platforms, Bitcoin OTC and Bitcoin Alpha, is used. Bitcoin trader behaviour in peer review networks is reduced to five behavioural features: attention, reputation, activity, fairness and goodness. The first three are derived from the data in a straightforward way. The last two are determined by using a state-of- the-art algorithm designed for trust/distrust networks. Trader types are extracted by clustering the traders based on the behavioural features. Due to timestamped data it is possible to define how the behaviour of Bitcoin traders evolve over time. Bitcoin peer review networks are represented as chronological aggregated snapshots of the underlying temporal system. Per each aggregated network, traders are clustered based on their behaviour. Cluster transitions provide information about how Bitcoin trader behaviour evolves over time. This work focuses especially on adverse behaviour. Adverse behaviour refers to giving unfair trust ratings to others or being distrusted by other traders, especially fair ones. The impact of receiving unfair ratings on a trader's behaviour is studied. In addition, it is studied if adversely behaving traders form communities. A community is a group of traders who have been rating each other. Behavioural clusters are also studied in relation to the most and the least central traders. The most central traders substantially contribute to the peer review network while the impact of the least central ones is negligible. The behavioural clusters show clear similarities between the datasets. There are trader types for which behaviour is exceptionally persistent. For well behaving traders it is common to remain as they are. Distrusted traders are likely to remain distrusted or disappear from the network, which can partly be explained by unfair negative treatment. Unfairly negatively rated traders can react to unfair treatment by becoming unfair themselves. Some of the most reputable traders have received their reputation from unfair positive ratings. Active and noticed traders with medium reputation behave in various ways in the future and are likely to stay in the network. In addition, it is observed that communities of unfairness and distrust emerge in Bitcoin peer review networks the same time with a burst of negative trust ratings. Surprisingly, the results on centrality show that the most well behaving traders become the least central. The most central traders in Bitcoin peer review networks are active and noticed traders who do not behave adversely

Incremental Strong Connectivity and 2-Connectivity in Directed Graphs

International audienceIn this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of those cuts. We give a conditional lower bound that provides evidence that our algorithms may be tight up to a sub-polynomial factors. As an additional result, with our approach we can also maintain dynamically the 2-vertex-connected components of a digraph during any sequence of edge insertions in a total of O(mn) time. This matches the bounds for the incremental maintenance of the 2-edge-connected components of a digraph