Random Information Spread in Networks

Let G=(V,E) be an undirected loopless graph with possible parallel edges and s and t be two vertices of G. Assume that vertex s is labelled at the initial time step and that every labelled vertex copies its labelling to neighbouring vertices along edges with one labelled endpoint independently with probability p in one time step. In this paper, we establish the equivalence between the expected s-t first arrival time of the above spread process and the notion of the stochastic shortest s-t path. Moreover, we give a short discussion of analytical results on special graphs including the complete graph and s-t series-parallel graphs. Finally, we propose some lower bounds for the expected s-t first arrival time.Comment: 17 pages, 1 figur

Weak ties: Subtle role of information diffusion in online social networks

As a social media, online social networks play a vital role in the social information diffusion. However, due to its unique complexity, the mechanism of the diffusion in online social networks is different from the ones in other types of networks and remains unclear to us. Meanwhile, few works have been done to reveal the coupled dynamics of both the structure and the diffusion of online social networks. To this end, in this paper, we propose a model to investigate how the structure is coupled with the diffusion in online social networks from the view of weak ties. Through numerical experiments on large-scale online social networks, we find that in contrast to some previous research results, selecting weak ties preferentially to republish cannot make the information diffuse quickly, while random selection can achieve this goal. However, when we remove the weak ties gradually, the coverage of the information will drop sharply even in the case of random selection. We also give a reasonable explanation for this by extra analysis and experiments. Finally, we conclude that weak ties play a subtle role in the information diffusion in online social networks. On one hand, they act as bridges to connect isolated local communities together and break through the local trapping of the information. On the other hand, selecting them as preferential paths to republish cannot help the information spread further in the network. As a result, weak ties might be of use in the control of the virus spread and the private information diffusion in real-world applications.Comment: Final version published in PR

Information mobility in complex networks

The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals. The mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix. The fractional time at which a network diffuses 50% of the information contained in its nodes (1/ k50 ) is also introduced. We then show that the scale-free random networks display better spread of information than the non scale-free ones. We study 38 real-world networks and analyze their performance in spreading information from their nodes. We find that some real-world networks perform even better than the scale-free networks with the same average degree and we point out some of the structural parameters that make this possible

Non-Conservative Diffusion and its Application to Social Network Analysis

The random walk is fundamental to modeling dynamic processes on networks. Metrics based on the random walk have been used in many applications from image processing to Web page ranking. However, how appropriate are random walks to modeling and analyzing social networks? We argue that unlike a random walk, which conserves the quantity diffusing on a network, many interesting social phenomena, such as the spread of information or disease on a social network, are fundamentally non-conservative. When an individual infects her neighbor with a virus, the total amount of infection increases. We classify diffusion processes as conservative and non-conservative and show how these differences impact the choice of metrics used for network analysis, as well as our understanding of network structure and behavior. We show that Alpha-Centrality, which mathematically describes non-conservative diffusion, leads to new insights into the behavior of spreading processes on networks. We give a scalable approximate algorithm for computing the Alpha-Centrality in a massive graph. We validate our approach on real-world online social networks of Digg. We show that a non-conservative metric, such as Alpha-Centrality, produces better agreement with empirical measure of influence than conservative metrics, such as PageRank. We hope that our investigation will inspire further exploration into the realms of conservative and non-conservative metrics in social network analysis

Influence Spread in Two-Layer Interdependent Networks: Designed Single-Layer or Random Two-Layer Initial Spreaders?

Influence spread in multi-layer interdependent networks (M-IDN) has been studied in the last few years; however, prior works mostly focused on the spread that is initiated in a single layer of an M-IDN. In real world scenarios, influence spread can happen concurrently among many or all components making up the topology of an M-IDN. This paper investigates the effectiveness of different influence spread strategies in M-IDNs by providing a comprehensive analysis of the time evolution of influence propagation given different initial spreader strategies. For this study we consider a two-layer interdependent network and a general probabilistic threshold influence spread model to evaluate the evolution of influence spread over time. For a given coupling scenario, we tested multiple interdependent topologies, composed of layers A and B, against four cases of initial spreader selection: (1) random initial spreaders in A, (2) random initial spreaders in both A and B, (3) targeted initial spreaders using degree centrality in A, and (4) targeted initial spreaders using degree centrality in both A and B. Our results indicate that the effectiveness of influence spread highly depends on network topologies, the way they are coupled, and our knowledge of the network structure — thus an initial spread starting in only A can be as effective as initial spread starting in both A and B concurrently. Similarly, random initial spread in multiple layers of an interdependent system can be more severe than a comparable initial spread in a single layer. Our results can be easily extended to different types of event propagation in multi-layer interdependent networks such as information/misinformation propagation in online social networks, disease propagation in offline social networks, and failure/attack propagation in cyber-physical systems