In this paper, we consider the friendship paradox in the context of random walks and paths. Among our results, we give an equality connecting long-range degree correlation, degree variability, and the degree-wise effect of additional steps for a random walk on a graph. Random paths are also considered, as well as applications to acquaintance sampling in the context of core-periphery structure.

Textual idea data from online crowdsourcing contains rich information of the concepts that underlie the original ideas and can be recombined to generate new ideas. But representing such information in a way that can stimulate new ideas is not a trivial task, because crowdsourced data are often vast and in unstructured natural languages. This paper introduces a method that uses natural language processing to summarize a massive number of idea descriptions and represents the underlying concept space as word clouds with a core-periphery structure to inspire recombinations of such concepts into new ideas. We report the use of this method in a real public-sector-sponsored project to explore ideas for future transportation system design. Word clouds that represent the concept space underlying original crowdsourced ideas are used as ideation aids and stimulate many new ideas with varied novelty, usefulness and feasibility. The new ideas suggest that the proposed method helps expand the idea space. Our analysis of these ideas and a survey with the designers who generated them shed light on how people perceive and use the word clouds as ideation aids and suggest future research directions.

Many real-world networks exhibit a multicores-periphery structure, with densely connected vertices in multiple cores surrounded by a general periphery of sparsely connected vertices. Identification of the multicores-periphery structure can provide a new lens to understand the structures and functions of various real-world networks. This paper defines the multicores-periphery structure and introduces an algorithm to identify the optimal partition of multiple cores and the periphery in general networks. We demonstrate the performance of our algorithm by applying it to a well-known social network and a patent technology network, which are best characterized by the multicores-periphery structure. The analyses also reveal the differences between our multicores-periphery detection algorithm and two state-of-the-art algorithms for detecting the single core-periphery structure and community structure.