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The heterogeneous information networks are omnipresent in real-world applications, which consist of multiple types of objects with various rich semantic meaningful links among them. Community discovery is an effective method to extract the hidden structures in networks. Usually, heterogeneous information networks are time-evolving, whose objects and links are dynamic and varying gradually. In such time-evolving heterogeneous information networks, community discovery is a challenging topic and quite more difficult than that in traditional static homogeneous information networks. In contrast to communities in traditional approaches, which only contain one type of objects and links, communities in heterogeneous information networks contain multiple types of dynamic objects and links. Recently, some studies focus on dynamic heterogeneous information networks and achieve some satisfactory results. However, they assume that heterogeneous information networks usually follow some simple schemas, such as bityped network and star network schema. In this paper, we propose a multityped community discovery method for time-evolving heterogeneous information networks with general network schemas. A tensor decomposition framework, which integrates tensor CP factorization with a temporal evolution regularization term, is designed to model the multityped communities and address their evolution. Experimental results on both synthetic and real-world datasets demonstrate the efficiency of our framework.

An open flow network is a weighted directed graph with a source and a sink, depicting flux distributions on networks in the steady state mode of an open flow system. Energetic food webs, economic input–output networks, and international trade networks are open flow network models of energy flows between species, money or value flows between industrial sectors, and goods flows between countries, respectively. An open flow network is different from a closed flow network because it considers the flows from or to the environment (the source and the sink). For instance, in energetic food webs, species obtain energy not only from other species but also from the environment (sunlight), and species also dissipate energy to the environment. Flow distances between any two nodes i and j are defined as the average number of transition steps of a random walker along the network from i to j . The conventional method for the calculation of the random walk distance on closed flow networks cannot be applied to open flow networks. Therefore, we derive novel explicit expressions for flow distances of open flow networks according to their underlying Markov matrix of the network in this paper. We apply flow distances to two types of empirical open flow networks, including energetic food webs and economic input–output networks. In energetic food webs, we visualize the trophic level of each species and compare flow distances with other distance metrics on the graph. In economic input–output networks, we rank sectors according to their average flow distances and cluster sectors into different industrial groups with strong connections. Other potential applications and mathematical properties are also discussed. To summarize, flow distance is a useful and powerful tool to study open flow systems.

With globalization, countries are more connected than before by trading flows, which currently amount to at least 36 trillion dollars. Interestingly, approximately 30-60 percent of global exports consist of intermediate products. Therefore, the trade flow network of a particular product with high added values can be regarded as a value chain. The problem is weather we can discriminate between these products based on their unique flow network structure. 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 $��$ 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, the flow networks of products with higher added values and complexity, such as machinery&transport equipment with larger exponents, are highlighted. These higher values indicate that their trade flow networks are more hierarchical. As a result, without extra data such as 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 solely by the trading network., 14 pages,7 figures