Understanding the influence of all nodes in a network

Abstract

Centrality measures such as the degree, k-shell, or eigenvalue centrality can identify a network's most influential nodes, but are rarely usefully accurate in quantifying the spreading power of the vast majority of nodes which are not highly influential. The spreading power of all network nodes is better explained by considering, from a continuous-time epidemiological perspective, the distribution of the force of infection each node generates. The resulting metric, the expected force, accurately quantifies node spreading power under all primary epidemiological models across a wide range of archetypical human contact networks. When node power is low, influence is a function of neighbor degree. As power increases, a node's own degree becomes more important. The strength of this relationship is modulated by network structure, being more pronounced in narrow, dense networks typical of social networking and weakening in broader, looser association networks such as the Internet. The expected force can be computed independently for individual nodes, making it applicable for networks whose adjacency matrix is dynamic, not well specified, or overwhelmingly large.

Bounds for degree-based network entropies

“…We start with applying Lemma 1 and also obtain Inequality (35). Now we use the well-known inequality a + b ≥ 2 ab, a, b > 0, (42) and set a αp i and b β.…”

“…Here the expected force accurately quantifies node spreading power under all primary epidemiological models across a wide range of archetypical human contact networks and is a node property derived from local network topology, independent of the rest of the network or any specific spreading process [35]. Therefore we continue studying these graph entropy measures (based on degree powers) by exploring their interrelations.…”

Super-Spreader Identification Using Meta-Centrality

“…Many methods, in particular centrality measure based methods, have been proposed in the past that aim to model and identify the most influential spreaders in complex networks. Among them, K-shell Decomposition method678 and Expected Force method9 have shown better performance than others under various epidemiological models. To evaluate the accuracy of the aforementioned measures various techniques has been employed.…”

Entropy of Weighted Graphs with Randi´c Weights

“…Mowshowitz [3] later studied mathematical properties of graph entropies measures thoroughly and also discussed special applications thereof. Graph entropy measures have been used in various disciplines, for example for characterizing graph patterns in biology, chemistry and computer science; see [7][8][9][10][11][12][13][14]. Thus, it is not surprising at all to realize that the term "graph entropy" has been defined in various ways.…”

“…Distance-based graph entropies [17,21] are also studied, which are related to the average distance and various Wiener indices [22][23][24][25][26][27][28][29][30][31][32]. The properties of graph entropies that are based on information functionals by using degree powers of graphs have been explored, too; see [13,33,34]. The degree power is one of the most important graph invariants and well studied in graph theory; its also related to the Zagreb index [35][36][37][38][39][40][41] and the zeroth-order Randić index [42][43][44].…”