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A key measure that has been used extensively in analyzing complex networks is the degree of a node (the number of the nodes neighbors). Because of its discrete nature, when the degree measure was used in analyzing weighted networks, weights were either ignored or thresholded in order to retain or disregard an edge. Therefore, despite its popularity, the degree measure fails to capture the disparity of interaction between a node and its neighbors. We introduce in this paper a generalization of the degree measure that addresses this limitation: the continuous node degree (C-degree). The C-degree of a node reflects how many neighbors are effectively being used, taking interaction disparity into account. More importantly, if a node interacts uniformly with its neighbors (no interaction disparity), we prove that the C-degree of the node becomes identical to the nodes (discrete) degree. We analyze four real-world weighted networks using the new measure and show that the C-degree distribution follows the power-law, similar to the traditional degree distribution, but with steeper decline. We also show that the ratio between the C-degree and the (discrete) degree follows a pattern that is common in the four studied networks.
Stars and cycles are basic structures in network construction. The former has been well studied in network analysis, while the latter attracted rare attention. A node together with its neighbors constitute a neighborhood star-structure where the basi
We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is
Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturi
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