Global consequences of local information biases in complex networks

2018-11-12Complex systems can be represented as networks of interacting entities or nodes. In numerous physical models on networks, dynamics are based on interactions that exclusively involve properties of a node's nearest neighbors. Local interactions among nodes in a complex network can lead to an astounding array of global behaviors. Examples include viral outbreaks and social contagions in social networks, cascading failures in the power grid and financial networks, synchronization of coupled oscillators, opinion dynamics and consensus formation in human groups. ❧ A node's local view of the network, however, may be systematically different from the global ground truth, which may affect global phenomena. Social scientists have identified one source of bias—the friendship paradox—which states that, on average, nodes have fewer connections, or smaller degree, than their neighbors. Recently, more interesting variations of the paradox were discovered. The strong friendship paradox states that most nodes have fewer connections than most of their neighbors. Unlike the original friendship paradox and its generalizations to attributes other than degree, the strong friendship paradox does not arise trivially as a result of sampling from skewed distributions. ❧ Strong friendship paradox can dramatically distort local information in a network, leading to the “majority illusion” paradox in which a globally rare attribute may be dramatically overrepresented in the local neighborhoods of many nodes. As consequence, many nodes will observe the majority of neighbors with the attribute, which can affect not only an individual node's behavior but also the collective phenomena unfolding on the network. Two key network properties determine the strength of the paradox in a network. The paradox in a network: 1. nodes with high connectivity are more likely bear that specific property, 2. nodes with high connectivity prefer to connect to nodes with low connectivity. By using these two correlations, we can quantify the global visibility of that specific property in a complex network. ❧ We also investigate the strength of the strong friendship paradox to estimate the amount of information distortion a node with a given connectivity experiences. To accurately model the strength of the strong friendship paradox requires a new structure property beyond the connectivity preference between two nodes mentioned above: what we defined as the correlation between node's neighbors or the neighbor assortativity. ❧ These paradoxes can influence results of social contagion. To verify this, we employ the Watt's threshold model, in which a node become active when some fraction of its neighbors are active. A mathematical theory with generating functions and tree-like assumption describes the size of contagious outbreaks. In most cases, there is a critical threshold that controls whether the outbreak is local or global (i.e. reaches a sizable fraction of the network). ❧ Interestingly we found that the outbreak behavior is non-monotonic with respect to networks assortativity. To explain this, we identify the weights of links between nodes that could be activated by a single neighbor are directly related to this phenomena. The vulnerable correlation can be then defined in the same manner. The outbreak threshold increases monotonically with the vulnerable correlation. ❧ Of the measures that define the properties of a network, most are based on the connectivity distribution of a single node or a pair of connected nodes. Not much discussion about higher order properties of network have been made so far. Our work elucidates how these properties affect local information bias a node experiences and its consequences on dynamic phenomena in networks, including dynamics of spreading processes