This paper investigates a particular spreading process, the spread of a rumour, on a community based network that is characterised by two parameters; the within-group connectivity, and the between-group connectivity and shows that such networks have different characteristics to small-world or random networks that are often used to model the types of systems.
Abstract
Many real-world networks have the characteristic that they are comprised of distinct groups or communities whose members contain many links within the community but with fewer connections to others. It is important to accurately model these types of networks to correctly predict the outcome of important spreading processes such as disease transmission, or the flow of information etc. Our motivating example is a network of traders within several investment institutions such as hedge funds. We assume an idealised scenario where traders within the same institution have many contacts and can share information quickly and easily but have fewer contacts to traders in other institutions, relying on personal networks, allowing for information to flow easily within a community and less-so between communities. In this paper we investigate a particular spreading process, the spread of a rumour, on a community based network that is characterised by two parameters; the within-group connectivity, and the between-group connectivity. We show that such networks have different characteristics to small-world or random networks that are often used to model the types of systems and that the network topology has a small but not insignificant effect on the spread of rumours on the network.
This work proposes a community-based preferential attachment hypergraph model with tunable modularity and a heavy-tailed degree distribution, reproducing key structural properties in real systems, and develops a hypergraph-based SAIR framework to describe epidemic dynamics with asymptomatic transmission.
Network epidemic simulation enables fine-grained understanding of epidemic behavior. However, empirical samples of interaction networks display properties that are challenging to capture with popular synthetic models of networks. Our empirical results show that epidemic spread behavior is sensitive to a form of multi-scale local structure that is absent in common baseline models, (e.g., Erdős–Rényi, Chung-Lu, etc). This structure critically impacts the effect of local quarantining and stops epidemic spread in samples of interaction networks, even when it cannot be halted in simple synthetic models of those networks. Insights from our analysis include how epidemics on networks with widespread multi-scale local structure are easier to mitigate, as well as characterizing which nodes are ultimately not likely to be infected. We demonstrate that this structure results from more than just local triangle structure in the network, and we illustrate processes based on homophily or social influence and random walks that suggest how this multi-scale local structure arises and use it to cleanly isolate intervention sensitivity to multi-scale local structure.
Omar Eldaghar, Michael W. Mahoney, D. Gleich· PLOS Complex Systems· 0 citations
It is shown, for the Susceptible-Infectious threshold process on temporal higher-order networks derived from human face-to-face interactions, that the contribution of each hyperlink can be quantified by a contagion backbone, whose dependency on the diffusion parameters is demonstrated and supported by theoretical analysis.
Shilun Zhang, A. Ceria, Huijuan Wang· Communications Physics· 0 citations
The Friendship Paradox states that, on average, your friends have more friends than you do. We extend this to common friends-those who appear in multiple people's friend lists. We show that the more people who share a common friend, the more connected that person tends to be, and we derive an expression quantifying this progression. In a regional Facebook network, a common friend to three randomly sampled individuals has on average more friends than 99.9% of the network. In a citation network, a source cited by any two of a random sample of papers has on average more citations than 99.99% of cited works. This power of common friends is most pronounced when few nodes hold disproportionate shares of ties, typical of networks involving superspreaders of disease, mega-influencers online, and highly connected nodes in neural networks. We discuss implications for network sampling, targeted interventions, social perception, and network dynamics.
Alec M. McGail, Scott Feld· Proceedings of the National...· 0 citations
The Internet, a living cell, a circle of friends, a billion-dollar construction project: these systems share almost nothing -- yet, drawn as networks, they look astonishingly alike. Each has a few giant hubs among a multitude of sparsely connected nodes, short paths between any two parts, dense local clustering, communities, and many redundant routes. For two decades such patterns have been credited to"preferential attachment,"the rich getting richer -- a rule that, taken literally, asks every newcomer to survey the whole network before it links. This book makes a simpler case, and defends it one mechanism at a time: the global regularities of real networks are not imposed from above but emerge from purely local rules, in which each new node acts only on a node it has reached and that node's immediate neighbours. A surfer following links, a friend introducing a friend, a gene copied with its connections -- none consults the network as a whole, yet each builds, in the aggregate, the full and unmistakable signature of a real complex system. Written for the curious reader as much as the specialist, with the ideas told in plain language and the mathematics set aside in boxes that can be skipped, it shows how citation graphs, the web, social ties, protein interactions, and project schedules all grow themselves from the same handful of local rules -- one local decision at a time.
This paper studies the problem of steering collective beliefs in social networks when only a small fraction of nodes can be directly influenced. We propose a sparse optimal control framework built on the Network Drift-Diffusion Model (NDDM). Two intervention mechanisms are considered: direct control and latent (indirect) control. To select which nodes to actuate, we compare six centrality measures---Degree, Betweenness, Eigenvector, Closeness, PageRank, and K-shell---and keep only the top 5\%--30\% as control inputs. The optimal feedback law follows from the Hamilton-Jacobi-Bellman (HJB) equation, which reduces to solving Riccati-type differential equations. We test our approach on Erdős-Rényi (ER), Barabási-Albert (BA), and Watts-Strogatz (WS) networks. The results show that the best centrality choice depends strongly on the network topology, and the system undergoes phase transitions as control parameters vary.
Bo Wang· Frontiers in Computing and I...· 0 citations
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