Merging in bipartite networks


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The bipartite network consists of donor nodes (red) with outgoing links and acceptor nodes (blue) with incoming links (nodes without links are grey). At each step two randomly chosen nodes merge. If the two nodes are of the same type, the links add up to one large node. If the nodes are of different type, links annihilate until the smaller node vanishes. This is interpreted as an energy burst visualized with a flash-size proportional to the burst. The size of the bursts is power-law distributed.

When pressing "Initialize" the network restarts at the vacuum state without any links.
Links are created by small excitations every step when two randomly chosen nodes get respectively one extra unit blue or red by addition of a link with a blue and a red end. The number of links between two nodes can be larger than one and can be estimated by the color of the plotted link. The more links a node has, the closer to the center of the network the node is plotted.


One way to interpret this merging model of a bipartite network is to consider the nodes as sunspots and the links as the associated magnetic field-lines in the solar atmosphere. Two sunspots of the same polarity merge to a larger sunspot and when two sunspots of different polarity merge the magnetic field-lines annihilate and energy is released. The size of these energy bursts have been measured two  be power-law distributed.

A simple model for self organization of bipartite networks.
Europhys. Lett., 67 (3), pp. 349-354 (2004)


Solar Flares as Cascades of Reconnecting Magnetic Loops
D. Hughes, M. Paczuski, R.O. Dendy, P. Helander and K.G. McClements.
Phys. Rev. Lett. 90, 131101 (2003).

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