ar X iv : c on d - m at / 0 30 66 22 v 1 2 4 Ju n 20 03 Bose - Einstein Condensation in Random Directed Networks
نویسنده
چکیده
O. Sotolongo-Costa and G. J. Rodgers Department of Theoretical Physics, Havana University, 10400 Havana,Cuba Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, U.K. and 3 Henri Poincare Chair of Complex Systems, Havana University. Abstract We consider the phenomenon of Bose-Einstein condensation in a random growing directed network. The network grows by the addition of vertices and edges. At each time step the network gains a vertex with probabilty p and an edge with probability 1− p. The new vertex has a fitness (a, b) with probability f(a, b). A vertex with fitness (a, b), in-degree i and out-degree j gains a new incoming edge with rate a(i + 1) and an outgoing edge with rate b(j + 1). The Bose-Einstein condensation occurs as a function of fitness distribution f(a, b).
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