Flows are ubiquitous in open complex systems. For example, energy flow, money flow, material flow, etc. However, there is no appropriate tool to analyze these flows on open systems. We develop one of the network analysis from ecology, which is called open flow networks. By modeling a flow system as a directed weighted network, we can depict distributions and structures of flows in a system. By adding two special nodes, source and sink, into the network, we can model open systems. We have applied this method on different fields including, online education and learning, online forum, web sites, international trading system, food webs, etc.
This study adopted an open flow network model and the associated distance metrics to gain an understanding of collective attention flow using clickstream data in a massive open online course. Various patterns and dynamics of attention flow were identified and are discussed here in relation to learning performance. The results show that the effective accumulation, circulation, and dissipation of attention flow are important contributors to academic attainment. Understanding the patterns and dynamics of attention flow will allow us to design cost-effective learning resources to prevent learners from becoming overloaded.
We apply flow distances to two kinds of empirical open flow networks, including energetic food webs and economic input-output network. In energetic food webs example, we visualize the trophic level of each species and compare flow distances with other distance metrics on graph. In input-output network, we rank sectors according to their average distances away other sectors, and cluster sectors into different groups. Some other potential applications and mathematical properties are also discussed. To summarize, flow distance is a useful and powerful tool to study open flow systems
This paper applies the flow analysis method developed in ecology to 638 trading flow networks of different products. We claim that the allometric scaling exponent n can be used to characterize the degree of hierarchicality of a flow network, i.e., whether the trading products flow on long hierarchical chains. Then, it is pointed out that the flow networks of products with higher added values and complexity like machinary, transport equipment etc. have larger exponents, meaning that their trade flow networks are more hierarchical. As a result, without the extra data like global input-output table, we can identify the product categories with higher complexity, and the relative importance of a country in the global value chain by the trading network solely.
Here, we propose a general model describing the effective distance of trade according to multilateral trade paths information and the structure of the trade flow network. Quantifying effective trade distance aims to identify the hidden resistance information from trade networks data, and then describe trade barriers. The results show that flow distance, hybrid by multi-path constraint, and international trade network contribute to the forecasting of trade flows. Meanwhile, we also analyze the role of flow distance in international trade from two perspectives of network science and econometric model. At the econometric model level, flow distance can collapse to the predicting results of geographic distance in the proper time lagging variable, which can also reflect that flow distance contains geographical factors. At the international trade network level, community structure detection by flow distances and flow space embedding instructed that the formation of international trade networks is the tradeoff of international specialization in the trade value chain and geographical aggregation. The methodology and results can be generalized to the study of all kinds of product trade systems.
The “ecological network analysis” can serve to reveal hidden allometries, the power law relationship between the throughflux and the indirect impact of node i, directly from the original flow networks without any need to cut edges in the network. The dissipation law, which is another significant scaling relationship between the energy dissipation (respiration) and the throughflow of any species, is also obtained from an analysis of the empirical flow networks. Interestingly, the exponents of the allometric law () and the dissipation law () show a strong relationship for both empirical and simulated flow networks. The dissipation law exponent , rather than the topology of the network, is the most important factors that affect the allometric exponent n .
By investigating 21 empirical weighted food webs as energy flow networks, we found several ubiquitous scaling behaviors. Two random variables Ai and Ci defined for each vertex i, representing the total flux (also called vertex intensity) and total indirect effect or energy store of i, were found to follow power law distributions with the exponents α ≈ 1.32 and β ≈ 1.33, respectively. Another scaling behavior is the power law relationship, Ci ∼ A η i , where η ≈ 1.02. This is known as the allometric scaling power law relationship because Ai can be treated as metabolism and Ci as the body mass of the sub-network rooted from the vertex i, according to the algorithm presented in this paper. Finally, a simple relationship among these power law exponents, η = (α−1)/(β −1), was mathematically derived and tested by the empirical food webs.
we propose a method to embed a large number of web sites into a high dimensional Euclidean space according to the novel concept of flow distance, which both considers connection topology between sites and collective click behaviors of users. With this geometric representation, we visualize the attention flow in the data set of Indiana university clickstream over one day. It turns out that all the websites can be embedded into a 20 dimensional ball, in which, close sites are always visited by users sequentially
This paper reviews the latest progress on the energy flow patterns, explanatory models for the allometric scaling and modelling approach of flow and network evolution dynamics in ecology. Furthermore, the possibility of generalizing these flow patterns, modelling approaches to other complex systems is discussed.