These are papers that caught my eye -- not guaranteed to be relevant or cutting edge. Symbols [C] denote lecture-sets where a paper is mentioned.
Abdullah et al. (2011): Viral Processes by Random Walks on Random Graphs.
Acemoglu et al. (2010): OPINION FLUCTUATIONS AND DISAGREEMENT IN SOCIAL NETWORKS . [G]
Aldous (1991): Threshold Limits for Cover Times. [E]
Aldous (2004): A Tractable Complex Network Model based on the Stochastic Mean-field Model of Distance.
Aldous - Bhamidi (2010): Edge Flows in the Complete Random-Lengths Network. [E]
Aldous-Shun (2010): Connected Spatial Networks over Random Points and a Route-Length Statistic.
Aldous (2010): More Uses of Exchangeability: Representations of Complex Random Structures. [E]
Aldous (2011): When Knowing Early Matters: Gossip, Percolation and Nash Equilibria . [E]
Bailey (1950): A Simple Stochastic Epidemic. [E]
Baronchelli et al. (2006): Sharp transition towards shared vocabularies in multi-agent systems. [H]
Britton (2010): Stochastic epidemic models: a survey.
Britton (2011): A weighted conﬁguration model and inhomogeneous epidemics.
Caputo - Liggett - Rochthammer (2009): Proof of Aldous' spectral gap conjecture. [C]
Castellano - Marsili - Vespignani (2000): Nonequilibrium phase transition in a model for social influence. [H]
Castellano - Fortunato - Loreto (2009): Statistical physics of social dynamics.
Chatterjee (2008): Contact processes on random graphs with power law degree distributions have critical value 0
Chatterjee - Durrett (2011) : Asymptotic Behavior of Aldous' Gossip Process. [E, St]
Chierichetti - Lattanzi - Panconesi (2009): Rumour spreading and graph conductance. [St]
Chierichetti (2010): Almost Tight Bounds for Rumour Spreading with Conductance
Cooper - Frieze - Radich (2009): Multiple Random Walks and Interacting Particle Systems. [D]
Cooper - Elsasser - Ono - Radzik (2012): Coalescing random walks and voting on graphs.
Cox (1989): Coalescing Random Walks and Voter Model Consensus Times on the Torus in $Z^d$. [D]
Cox (2010): INTERMEDIATE RANGE MIGRATION IN THE TWO-DIMENSIONAL STEPPING STONE MODEL
Davis (1993): The expected length of a shortest path
Deijfen (2010): Epidemics and vaccination on weighted graphs
Ding - Lubetzky - Peres (2008): Total variation cutoff in birth-and-death chains. [E]
Ding - Lee - Peres (2010): Cover times, blanket times, and majorizing measures. [B]
Draief and Massouli (2007): Epidemics and Rumours in Complex Networks (Partial version of this 2010 monograph)
Durrett (2007): Two Phase Transitions for the Contact Process on Small Worlds
Durrett (2010): Some features of the spread of epidemics and information on a random graph
Elsasser (2009): COVER TIME AND BROADCAST TIME
Frieze (1985): On the value of a random minimum spanning tree problem. [E]
Gao (2009): Multicasting in Delay Tolerant Networks: A Social Network Perspective
Granovetter (1973): On Strength of Weak Ties
van der Hofstad - Hooghiemstar - van Miegham (2002): The flooding time in random graphs. [E]
Holme et al. (2003): Prisoners' dilemma in real-world acquaintance networks: Spikes and quasi-equilibria induced by the interplay between structure and dynamics. [H]
Janson (1999): One, two and three times $\log n/n$ for paths in a complete graph with random weights . [E}
Karrer - Newman (2010): A message passing approach for general epidemic models. [F, St]
Kempe (2004): Spatial gossip and resource location protocols
Kempe (2010): Structure and Dynamics of Information in Networks . (Lecture notes)
Lapus (2010): Random Information Spread in Networks
Leon - Perron (2004): Optimal Hoeffding bounds for discrete reversible Markov chains. [B]
Lelarge (2011): Diffusion and Cascading Behavior in Random Networks. [F]
Leskovec et al (2008): Statistical Properties of Community Structure in Large Social and Information Networks
Liu (2009): An Optimal Probabilistic Forwarding Protocol in Delay Tolerant Networks
Manshadi - Saberi (2011): Prisoner's Dilemma on Graphs with Large Girth. [D]
Marvel et al (2011): Continuous-time model of structural balance
Montenegro - Tetail (2006): Mathematical Aspects of Mixing Times in Markov Chains. [B]
Mossel - Schoenbeck (2010): Reaching Consensus on Social Networks. [E]
Mountford et al (2012): EXPONENTIAL EXTINCTION TIME OF THE CONTACT PROCESS ON FINITE GRAPHS.
Nowak - May (1993): The spatial dilemmas of evolution. [H]
Oliveira (2010): On the coalescence time of reversible random walks. [D]
Oliveira (2011): Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk. [C]
Oliveira (2012): Mean field conditions for coalescing random walks.
Peres - Sousi (2012): Mixing times are hitting times of large sets.
Picu (2010): Minimum Expected *-cast Time in DTNs
Shah (2008): Gossip Algorithms. [C,E]
Sood - Antal - Radner (2008): Voter models on heterogeneous networks . [D]
Stauffer (2004): Probabilistic Heuristics for Disseminating Information in Networks
Wastlund (2010): The mean field traveling salesman and related problems. [E]
Watts (2002): A Simple Model of Global Cascades on Random Networks. [F]