Abstract
Diffusion of knowledge is expected to be huge when agents are open minded. The report concerns a more difficult diffusion case when communities are made of stubborn agents. Communities having markedly different opinions are for example the Neocreationist and Intelligent Design Proponents (IDP), on one hand, and the Darwinian Evolution Defenders (DED), on the other hand. The case of knowledge diffusion within such communities is studied here on a network based on an adjacency matrix built from time ordered selected quotations of agents, whence for inter- and intra-communities. The network is intrinsically directed and not necessarily reciprocal. Thus, the adjacency matrices have complex eigenvalues, the eigenvectors present complex components. A quantification of the slow-down or speed-up effects of information diffusion in such temporal networks, with non-Markovian contact sequences, can be made by comparing the real time dependent (directed) network to its counterpart, the time aggregated (undirected) network, - which has real eigenvalues. In order to do so, small world networks which both contain an $odd$ number of nodes are studied and compared to similar networks with an $even$ number of nodes. It is found that (i) the diffusion of knowledge is more difficult on the largest networks, (ii) the network size influences the slowing-down or speeding-up diffusion process. Interestingly, it is observed that (iii) the diffusion of knowledge is slower in IDP and faster in DED communities. It is suggested that the finding can be "rationalized", if some "scientific quality" and "publication habit" is attributed to the agents, as common sense would guess. This finding offers some opening discussion toward tying scientific knowledge to belief.
Highlights
Locating, structuring, thereafter simulating stylized facts on the diffusion of knowledge becomes increasingly difficult due to the huge accumulation of big data
Individuals leading the transfer of opinion between Intelligent Design Proponents (IDP) and DED communities can be identified by analyzing the number of directed triangles and of undirected links of the citation network
It has been shown that changes of diffusion dynamics in temporal networks as compared to their static counterparts are due to the change of connectedness or conductance of the corresponding second-order aggregate network
Summary
Locating, structuring, thereafter simulating stylized facts on the diffusion of knowledge becomes increasingly difficult (see e.g., [1]) due to the huge accumulation of big data. It is imposed that the nodes belong to two communities made of stubborn agents, in order to keep a systematic topological structure, i.e., the diffusion of knowledge is supposed to exist, but without a modification of the state of the recipient, - as when insults are exchanged between agents Such communities having markedly different opinions have been previously studied in general frameworks [9,10,11]. The case of knowledge diffusion within such communities is studied from time ordered selected quotations of agents, whence after building networks, each mimicked by its adjacency matrix, with ranks and rows ordered to define inter- and intracommunity links These networks are intrinsically directed and not necessarily reciprocal. A quantification of the slow-down or speed-up effects of information diffusion in such temporal networks, with nonMarkovian contact sequences, can be made by comparing the real time dependent (directed) network to its counterpart, the time aggregated (undirected) network, - which has real eigenvalues; see Sections 3 and 4
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