Locating influential nodes via dynamics-sensitive centrality

With great theoretical and practical significance, locating influential nodes of complex networks is a promising issues. In this paper, we propose a dynamics-sensitive (DS) centrality that integrates topological features and dynamical properties. The DS centrality can be directly applied in locating influential spreaders. According to the empirical results on four real networks for both susceptible-infected-recovered (SIR) and susceptible-infected (SI) spreading models, the DS centrality is much more accurate than degree, $k$-shell index and eigenvector centrality.Comment: 6 pages, 1 table and 2 figure

Uncovering the popularity mechanisms for Facebook applications

Understanding the popularity dynamics of online application(App) is significant for the online social systems. In this paper, by dividing the Facebook Apps into different groups in terms of their popularities, we empirically investigate the popularity dynamics for different kinds of Facebook Apps. Then, taking into account the influence of cumulative and recent popularities on the user choice, we present a model to regenerate the growth of popularity for different App groups. The experimental results of 917 Facebook Apps show that as the popularities of Facebook Apps increase, the recent popularity plays more important role. Specifically, the recent popularity plays more important role in regenerating the popularity dynamics for more popular Apps, and the cumulative popularity plays more important role for unpopular Apps. We also conduct temporal analysis on the growth characteristic of individual App by comparing the increment at each time with the average of historical records. The results show that the growth of more popular App tends to fluctuate more greatly. Our work may shed some lights for deeply understanding the popularity mechanism for online applications

Lightning network: a second path towards centralisation of the Bitcoin economy

The Bitcoin Lightning Network (BLN), a so-called "second layer" payment protocol, was launched in 2018 to scale up the number of transactions between Bitcoin owners. In this paper, we analyse the structure of the BLN over a period of 18 months, ranging from 12th January 2018 to 17th July 2019. Here, we consider three representations of the BLN: the daily snapshot one, the weekly snapshot one and the daily-block snapshot one. By studying the topological properties of the three representations above, we find that the total volume of transacted bitcoins approximately grows as the square of the network size; however, despite the huge activity characterising the BLN, the bitcoins distribution is very unequal: the average Gini coefficient of the node strengths (computed across the entire history of the Bitcoin Lightning Network) is, in fact, ~0.88 causing the 10% (50%) of the nodes to hold the 80% (99%) of the bitcoins at stake in the BLN (on average, across the entire period). This concentration brings up the question of which minimalist network model allows us to explain the network topological structure. Like for other economic systems, we hypothesise that local properties of nodes, like the degree, ultimately determine part of its characteristics. Therefore, we have tested the goodness of the Undirected Binary Configuration Model (UBCM) in reproducing the structural features of the BLN: the UBCM recovers the disassortative and the hierarchical character of the BLN but underestimates the centrality of nodes; this suggests that the BLN is becoming an increasingly centralised network, more and more compatible with a core-periphery structure. Further inspection of the resilience of the BLN shows that removing hubs leads to the collapse of the network into many components, an evidence suggesting that this network may be a target for the so-called split attacks.Comment: 11 pages, 7 figure

Rank the spreading influence of nodes using dynamic Markov process

Ranking the spreading influence of nodes is of great importance in practice and research. The key to ranking a node’s spreading ability is to evaluate the fraction of susceptible nodes being infected by the target node during the outbreak, i.e. the outbreak size. In this paper, we present a dynamic Markov process (DMP) method by integrating the Markov chain and the spreading process to evaluate the outbreak size of the initial spreader. Following the idea of the Markov process, this method solves the problem of nonlinear coupling by adjusting the state transition matrix and evaluating the probability of the susceptible node being infected by its infected neighbors. We have employed the susceptible-infected-recovered and susceptible-infected-susceptible models to test this method on real-world static and temporal networks. Our results indicate that the DMP method could evaluate the nodes’ outbreak sizes more accurately than previous methods for both single and multi-spreaders. Besides, it can also be employed to rank the influence of nodes accurately during the spreading process

Predicting Nodal Influence via Local Iterative Metrics

Nodal spreading influence is the capability of a node to activate the rest of the network when it is the seed of spreading. Combining nodal properties (centrality metrics) derived from local and global topological information respectively is shown to better predict nodal influence than a single metric. In this work, we investigate to what extent local and global topological information around a node contributes to the prediction of nodal influence and whether relatively local information is sufficient for the prediction. We show that by leveraging the iterative process used to derives a classical nodal centrality such as eigenvector centrality, we can define an iterative metric set that progressively incorporates more global information around the node. We propose to predict nodal influence using an iterative metric set that consists of an iterative metric from order $1$ to $K$ that are produced in an iterative process, encoding gradually more global information as $K$ increases. Three iterative metrics are considered, which converge to three classical node centrality metrics respectively. Our results show that for each of the three iterative metrics, the prediction quality is close to optimal when the metric of relatively low orders ($K\sim4$) are included and increases only marginally when further increasing $K$. The best performing iterative metric set shows comparable prediction quality to the benchmark that combines seven centrality metrics, in both real-world networks and synthetic networks with community structures. Our findings are further explained via the correlation between an iterative metric and nodal influence, the convergence of iterative metrics and network properties

Identifying influential spreaders by gravity model

Identifying influential spreaders in complex networks is crucial in understanding, controlling and accelerating spreading processes for diseases, information, innovations, behaviors, and so on. Inspired by the gravity law, we propose a gravity model that utilizes both neighborhood information and path information to measure a node’s importance in spreading dynamics. In order to reduce the accumulated errors caused by interactions at distance and to lower the computational complexity, a local version of the gravity model is further proposed by introducing a truncation radius. Empirical analyses of the Susceptible-Infected-Recovered (SIR) spreading dynamics on fourteen real networks show that the gravity model and the local gravity model perform very competitively in comparison with well-known state-of-the-art methods. For the local gravity model, the empirical results suggest an approximately linear relation between the optimal truncation radius and the average distance of the network