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]