Newman: Vertices and Edges in a Network

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Vertex (pl. vertices): The fundamental unit of a network, also called a site (physics), a node (computer science), or an actor (sociology).

Edge: The line connecting two vertices. Also called a bond (physics), a link (computer science), or a tie (sociology).” (p. 5) #Newman #network #vertex #edge #bond #link

Newman, Mark E. J., The Structure and Function of Complex Networks, in: SIAM Review 45 (2003), 167–256.

Newman: What is a network?

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“A network is a set of items, which we will call vertices or sometimes nodes, with connections between them, called edges. Systems taking the form of networks (also called “graphs” in much of the mathematical literature) abound in the world.” (p. 2) #Newman #network #system

Newman, Mark E. J., The Structure and Function of Complex Networks, in: SIAM Review 45 (2003), 167–256.

Zheng: Phase Transition

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„Percolation transition, the transition from a disconnected state to a connected one, has been regarded as a fundamental model of phase transitions in nonequilibrium systems. One of the most fundamental characteristics of a phase transition is its order, i.e., whether the macroscopic quantity affects changes continuously or discontinuously at the transition point. The percolation phase transitions in random networks were originally considered to be robust continuous phase transitions.“ (p. vii) #Zheng #percolation #PhaseTransition #random #network

Zheng, Zhiming, Supervisor’s Foreword, in: Explosive Percolation in Random Networks. Berlin/Heidelberg: Springer 2014, vii–viii.