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Illustration of the process to compute the product roles from the recipe data, where cyan squares are recipe nodes, orange circles are ingredient nodes, red circles are product nodes, the line thickness corresponds to how high the corresponding scores are, and l 0 substitute roles, l complement role(s) and l 1 substitute roles are shown as groups of product nodes in the purple dashed circles, green dashed polygon(s) and blue dashed circles, respectively
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The complementarity and substitutability between products are essential concepts in retail and marketing. Qualitatively, two products are said to be substitutable if a customer can replace one product by the other, while they are complementary if they tend to be bought together. In this article, we take a network perspective to help automatically i...
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... the role assignments (of products) from both datasets, where l complement roles and l 1 substitute roles (from the recipe data) are obtained from applying community detection on W (cr) and W (sr) , respectively. We construct extra l 0 substitute roles by grouping together products that are matched to the same ingredients, for reference; see Fig. 3 for ...
Citations
... Chen et al. (2020) follow the previous two approaches and use the complementarity and exchangeability measures based on a low-dimensional space of products. Tian et al. (2021) study product relationships in a bipartite product-purchase network and define the substitutability and complementarity measures as cosine similarity. ...
... High values of ρ ij are caused by similar purchase patterns of products i and j with respect to the other products k; more specifically, by similar sets of complements of products i and j. Similarly to Ruiz et al. (2020) and Tian et al. (2021), we attribute this behavior to substitutes. Values of ρ ij near zero indicate independent products. ...
We propose a measure of product substitutability based on correlation of common purchases, which is fast to compute and easy to interpret. In an empirical study of a drugstore retail chain, we demonstrate its properties, compare it to a similarly simple measure of product complementarity, and use it to find small clusters of substitutes.
The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein interactions (PPI) are driven by complementarity (differences and synergy). Here we show that the principle of complementarity is linked to the abundance of quadrangles (4-cycles) and dense bipartite-like subgraphs. We link both principles to their characteristic motifs and introduce two families of coefficients of: (1) structural similarity, which generalize local clustering and closure coefficients and capture the full spectrum of similarity-driven structures; (2) structural complementarity, defined analogously but based on quadrangles instead of triangles. Using multiple social and biological networks, we demonstrate that the coefficients capture structural properties related to meaningful domain-specific phenomena. We show that they allow distinguishing between different kinds of social relations as well as measuring an increasing structural diversity of PPI networks across the tree of life. Our results indicate that some types of relations are better explained by complementarity than homophily, and may be useful for improving existing link prediction methods. We also introduce a Python package implementing efficient algorithms for calculating the proposed coefficients.
In the context of the Bitcoin market and its virtual investment communities, this paper demonstrates that both similarity and dissimilarity in social media messages’ contents can be associated with high quotation probability among them. This finding advocates new understandings beyond the mainstream conclusion that network connections increase with similarity. It is also found that message networks offer significant implications to distinguish between accurate information and noise. Evidence shows that popular messages frequently quoted by others and redundant messages confirmed from different sources contain more accurate information for Bitcoin market predictions. Theoretical contributions and practical implications are discussed.
