The social network maintained by a focal individual, or ego, is intrinsically dynamic and typically exhibits some turnover in membership over time as personal circumstances change. However, the consequences of such changes on the distribution of an e
gos network ties are not well understood. Here we use a unique 18-month data set that combines mobile phone calls and survey data to track changes in the ego networks and communication patterns of students making the transition from school to university or work. Our analysis reveals that individuals display a distinctive and robust social signature, captured by how interactions are distributed across different alters. Notably, for a given ego, these social signatures tend to persist over time, despite considerable turnover in the identity of alters in the ego network. Thus as new network members are added, some old network members are either replaced or receive fewer calls, preserving the overall distribution of calls across network members. This is likely to reflect the consequences of finite resources such as the time available for communication, the cognitive and emotional effort required to sustain close relationships, and the ability to make emotional investments.
Tools of the theory of critical phenomena, namely the scaling analysis and universality, are argued to be applicable to large complex web-like network structures. Using a detailed analysis of the real data of the International Trade Network we argue
that the scaled link weight distribution has an approximate log-normal distribution which remains robust over a period of 53 years. Another universal feature is observed in the power-law growth of the trade strength with gross domestic product, the exponent being similar for all countries. Using the rich-club coefficient measure of the weighted networks it has been shown that the size of the rich-club controlling half of the worlds trade is actually shrinking. While the gravity law is known to describe well the social interactions in the static networks of population migration, international trade, etc, here for the first time we studied a non-conservative dynamical model based on the gravity law which excellently reproduced many empirical features of the ITN.
Detecting community structure in real-world networks is a challenging problem. Recently, it has been shown that the resolution of methods based on optimizing a modularity measure or a corresponding energy is limited; communities with sizes below some
threshold remain unresolved. One possibility to go around this problem is to vary the threshold by using a tuning parameter, and investigate the community structure at variable resolutions. Here, we analyze the resolution limit and multiresolution behavior for two different methods: a q-state Potts method proposed by Reichard and Bornholdt, and a recent multiresolution method by Arenas, Fernandez, and Gomez. These methods are studied analytically, and applied to three test networks using simulated annealing.
Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By tuning a
model parameter governing the importance of weights, the resulting networks undergo a gradual structural transition from a module free topology to one with communities. The model also reproduces many features of large social networks, including the weak links property.
