中介驱动型依恋网络中的程度分布、等级规模分布与领导持续性
Degree Distribution, Rank-size Distribution, and Leadership Persistence in Mediation-Driven Attachment Networks
摘要：
我们研究了一类网络的增长，其中一个新的节点首先随机选择一个调解人，并与$m$随机选择的邻居的调解人在每个时间步连接。我们发现，在这样一个中介驱动的附件（MDA）网络的度分布表现出幂律$P(k)\sim k^{-γ(m)}$的指数依赖于$m$的频谱。为了理解MDA和Barabási-Albert（BA）网络之间的对比，我们讨论了它们的秩-大小分布。要量化多久的领导者，具有最大程度的节点，坚持在其领导的网络的发展，我们调查的领导持续概率$F(τ)$，即概率，领导者保持其领导的时间$τ$。我们发现，在MDA网络中，$F(τ)\sim τ^{-θ(m)}$的持续指数为$θ(m) \approx 1.51 \ \forall \ m$，在BA网络中，$F(τ)\sim τ^{-θ(m)}$的持续指数为$θ(m) \rightarrow 1.53$的持续指数为$m$.
英文摘要：
We investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with $m$ randomly chosen neighbors of the mediator at each time step. We show that degree distribution in such a mediation-driven attachment (MDA) network exhibits power-law $P(k)\sim k^{-γ(m)}$ with a spectrum of exponents depending on $m$. To appreciate the contrast between MDA and Barabási-Albert (BA) networks, we then discuss their rank-size distribution. To quantify how long a leader, the node with the maximum degree, persists in its leadership as the network evolves, we investigate the leadership persistence probability $F(τ)$ i.e. the probability that a leader retains its leadership up to time $τ$. We find that it exhibits a power-law $F(τ)\sim τ^{-θ(m)}$ with persistence exponent $θ(m) \approx 1.51 \ \forall \ m$ in the MDA networks and $θ(m) \rightarrow 1.53$ exponentially with $m$ in the BA networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
