Proteins are essential macromolecules of life that carry out most cellular processes. Since proteins aggregate to perform function, and since protein-protein interaction (PPI) networks model these aggregations, one would expect uncover new biology from PPI network topology. Hence, using predict protein function role pathways in disease has received attention. A debate remains open about whether properties "biologically central (BC)" genes (i.e., their products), such as those involved aging,...

_We introduce a new graph parameter called the burning number, inspired by contact processes on graphs such as bootstrap percolation, and searching paradigms Firefighter. The number measures speed of spread contagion in graph; lower faster spreads. We provide properties including characterizations bounds. is computed for several classes, derived generated Iterated Local Transitivity model social networks_.

We present a new stochastic model for complex networks, based on spatial embedding of the nodes, called _spatial preferred attachment_ (SPA) model. In SPA model, nodes have influence regions varying size, and may link to node only if they fall within its region. The models background knowledge or identity node, which will environment. our can determine their environment local network. prove that gives power-law in-degree distribution, with exponent in [2,∞) depending parameters,...

Meyniel's conjecture is one of the deepest open problems on cop number a graph.It states that for connected graphWhile largely ignored over 20 years, receiving increasing attention.We survey origins and recent developments towards solution conjecture.We present some new results Meyniel extremal families containing graphs order n satisfying c(G) ≥ d √ n, where constant.

The Common Out-Neighbor (or CON) score quantifies shared influence through outgoing links in competitive contexts. A dynamic analysis of competition networks reveals the CON as a powerful predictor node rankings. Defined first-order and second-order forms, captures both direct indirect interactions, offering comprehensive metric for evaluating influence. Using datasets from Survivor, Chess.com, Dota~2 online gaming competitions, directed are constructed, is integrated into supervised machine...

We present a deterministic model for online social networks (OSNs) based on transitivity and local knowledge in interactions. In the iterated (ILT) model, at each time step every existing node _x_, new appears that joins to closed neighbor set of _x_. The ILT provably satisfies number both global properties have been observed OSNs other real-world complex networks, such as densification power law, decreasing average distance, higher clustering than random graphs with same degree....

We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. find a network model with nodes links sampled from an m-dimensional metric space power-law distributed influence regions best fits samples real-world networks when m scales logarithmically number network. This supports logarithmic dimension hypothesis, we provide evidence two different Facebook LinkedIn. Further, employ methods for confirming hypothesis: first uses distribution...

Pursuit-evasion games, such as the game of Cops and Robbers, are a simplified model for network security. In this game, cops try to capture robber loose on vertices network. The minimum number required win graph _G_ is its number. We present asymptotic results Robbers played in various stochastic models, _G_(_n, p_) with nonconstant _p_ random power-law graphs. find bounds cop large range function _n_. prove that graphs _n_ asymptotically almost surely Θ(_n_). core investigated, it proved be...

We study the link structure of online social networks (OSNs) and introduce a new model for such that may help in inferring their hidden underlying reality. In geo-protean (GEO-P) OSNs, nodes are identified with points Euclidean space, edges stochastically generated by mixture relative distance ranking function. With high probability, GEO-P generates graphs satisfying many observed properties as power-law degree distributions, small-world property, densification power law, bad spectral...

Abstract We investigate the cop number of graphs based on combinatorial designs. Incidence graphs, point and block intersection are studied, with an emphasis finding families large number. generalize known results Meyniel extremal by supplying bounds incidence transversal designs, certain G ‐designs, BIBDs Families diameter 2, C 4 ‐free, unbounded chromatic described conjectured asymptotically maximum