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With the implementation of European integration policies such as the single market, the Euro and the Schengen Visa, the EU member states are developing closer economic ties through tourism, and their level of tourism integration is constantly improving. Taking the 28 EU member states as research objects, this paper constructs a tourism economic connection network among them, measures the strength of their tourism economic connections from 1995 to 2018 by using the modified gravity model and social network method, and analyzes the spatial structure characteristics and effects of the EU tourism economy. The results are as follows: (1) The tourism economic ties of EU member states are growing increasingly close, enhancing network stability. (2) Germany, France, Italy, Austria and the United Kingdom are the top five countries in the degree centrality and closeness centrality rankings, meaning that they are located in the center of the network and have great influence, and the network is becoming increasingly concentrated. Germany, Italy, Sweden, Austria and France play an important intermediary role in the network, and the centrality of most member states has increased. (3) The core areas are mainly concentrated in Western Europe, Southern Europe, Mediterranean mainland countries and Central Europe, while the marginal areas are mainly concentrated in Eastern Europe, Northern Europe and Mediterranean island countries; the network connection density of the core area, the network connection density of the marginal area, and the network connection density between the core and marginal area overall show an increasing trend. (4) Improvements in the complete network connectedness and a reduction in graph efficiency can significantly reduce differences in EU tourism economic development levels and improve spatial equity.